I finally decided to tackle Sherlock's fake death.
Before going into details, I thought a summary of the aids he could have had would be useful:
People which could have helped:
Homeless network
Molly
Mycroft
Lestrade
Mike
People definitely unaware of how he pulled it off:
Mrs. Hudson
John
Sniper
Things he had with him ( within reach):
Moriarty's corpse (who must be dead as otherwise he'd have interrupted Sherlock's plan to fake his death)
Phone (Moriarty)
Phone (Sherlock)
Additionally, we know that Sherlock suffered no serious injuries as he's able to walk in the last scene.
No serious injuries - he could not have jumped the whole way. Even with a good rescue net, only jumps from roughly 8 metres ( 26 foot) can be eased, with and without support. Just an example, I do not believe there was a rescue net. Assuming he jumped "all the way", it must be a method which would allow him to a) leave the scene in a rush, and b) without breaking both his legs.
He could have been hurt and already recovered in the last scene of the episode!
Maybe, but: While we are not shown what kind of casket is buried or whether it's an urn, we see John grieving at the graveyard. The episode is depicted to occur after the therapist visit. In the beginning of Reichenbach Fall, he talks to his therapist, mentioning that it should be obvious why he's there, at least from the papers. Thus Sherlock's death cannot have happened more than one or two weeks ago if it still causes headlines. Sherlock's appearance in the graveyard likely has to happen shortly after, even if there's already a headstone. Two weeks, maybe three are not sufficient to heal a broken leg.
Now, looking at the episode as a whole: one thing clearly stands out.
Moriarty ends up in prison - and gets out. Because "he chose to be there. It is part of his scheme" as Sherlock put it.
Sherlock ends up on the rooftop meeting Moriarty - and survives. Because he chose to be there. It is part of his scheme?
To me, Sherlock's fake death was clearly inspired by Irene's precedent and Moriarty's lesson. Lesson? Yes, during their tea time session, Moriarty taught Sherlock one important thing: to cheat best, use people. Or in his words: All it takes is some willing participants.
Everything can be pulled off with the help of some additional hands. It is remarkable that Sherlock faked his death, especially since he had to rely on somebody else. Not his usual style. Even with Mycroft he often was more than reluctant to include him on his schemes.
Interestingly, this tea time scene also has Moriarty say "I owe you a fall". Enough hint for somebody like Sherlock to figure out his "destiny". Even if it had taken him longer to understand Moriarty's intentions, he still would have had time to plot something. Two months, to be exact. Molly deduced that Sherlock was looking "sad". If she was wrong, it wouldn't have made it into the script. So he was sad - or rather, worried? Curious, isn't it, that this statement followed Sherlock's mumbling about 'I owe you'?
He knew he'd "fall". Once again, the question from above: Because he chose to be there. It is part of his scheme?
Sherlock chose Bart's rooftop, interesting, isn't it?
I owe you - Moriarty's message more than once:
1. Ripe, red apple - ripe apples fall from trees - in connection with Grimm's fairytales, there is one red apple featuring prominently; the story is called "Snow White". She took a bite from the poisoned apple and appeared dead - but came back to life when she coughed it out. Could hint that Sherlock took something to appear dead, but just a thought. Likely, one could argue that he took a bite from Moriarty's apple, he applied some of Moriarty's strategies and created his own survival strategy.
2. Building; when Sherlock looks out of the window, there's another love message from Moriarty.
This I actually consider most important: He's in Bart's while seeing the message. Time still open, yet the place of his fall seems set.
Concerning how he did it and things that struck me while watching the episode:
1. Another Sherlock-quote from the episode: "Anybody can walk in anywhere - if they picked the right moment."
Interestingly, this might even give us a pointer: Anybody can walk anywhere 'out'/'in' - if they picked the right moment. While everybody's crowding the corpse, during this mess and the confusion, nobody would have paid much attention to anything but the corpse. Sherlock, as the quote indicates, is aware of that fact - and has been made aware of it recently. Something at the front of his mind, something he'd remember while plotting his death. No matter how he faked his death, he'd need to be found by the right people. To leave the scene, while minimizing the possibility of being spotted. So, picking the right moment, the chaos after the body fell - who took his body away? Two paramedics and two business men. More about that later on.
2. The girl screams when she sees Sherlock - while she clearly was fine with Lestrade before. Two possibilities I see: either it's the black hair (reminds her of the 'bad guy') or Sherlock's face. I believe in the latter. A mask. Of course both are likely, but the mask would make sense. Sherlock is clever enough to pick up on the fact why the girl might react so strongly upon seeing him. And use Moriarty's idea. In modern age, realistic masks exist and with a mask, he could have hidden the true identity of the "victim". Making, for example, Moriarty into "himself", long enough to fool the undertaker?
The possibility of a mask - one thing I'd like to keep in mind. Just a thought that hit me unexpectedly.
3. Molly offers him her help - Sherlock later confronts her.
It is clear that she in some way is involved in his fake death. Maybe only as the person identifying the corpse, maybe as the person doing the postmortem, maybe she also helped with the corpse preparation and gave him "fake blood".
Molly is part of his scheme.
4. Ever noticed the black, small ball he's playing with during the scene where John finds him in the mortuary?
Usually used to stop one's pulse by pressing it under one's armpit. To appear dead.
A potential prop, I'd say. Especially since this is the scene where he messages Moriarty and tells him to come to the rooftop. Final preparation complete.
When he leaves the room, there's a clinkering sound. Like a vial - full of blood?
I guess he took the ball and a vial of blood with him to the rooftop.
5. John gets agitated over Mrs. Hudson's "injury", Sherlock doesn't react. As if he expected it. I think it was not Moriarty who initiated the fake call but Sherlock. To keep John away. Who's behind the call, though? Not Molly, she doesn't have that power. Sherlock needs another participant. Mycroft? Lestrade? Both would have the power to get a fake caller.
6. Sherlock's behavior on the rooftop:
This will be a long paragraph. First things first: he reacts agitated, rather interesting, isn't it? Especially since I firmly believe he was aware of Moriarty's plans beforehand. So I shifted my focus onto what information he gets by pressuring Jim. That the code was fake, that lots of people are after him, that there are three snipers and on whom they are.
Now upon him hesitating to jump: asking Jim for some time? Must be a reason behind that, especially since he's prepared to 'jump'. Which? Well, while looking down, you can see that there's a bus blocking the street. Behind the bus, there's another car, that seems really keen on getting where the bus stands. I consider that car important. The distance still seems rather far for a person to jump. Next thing I noticed: there's a person on the bank. Perhaps a "participant", perhaps not. Could be an additional helping hand, however. The street corner also provides some cover from other audience. Those are the hard facts: bus blocking the bus stop, big car behind it, person sitting on a bench, not the best place for a lot of audience (some might consider this an advantage).
Sherlock asks Jim for a moment - not out of sentiment, I think. Rather to allow the bus to leave so that the car behind it can take position. Then he begins to laugh - either because the bus finally left, so everything is going by plan or because he needs to buy more time.
What he could not have anticipated: Moriarty shooting himself. Sherlock's not dumb, he would have checked for a pulse, for any sign of life still in the body. No, I believe Jim killed himself. Is dead for good. Actually, I think this complicated his plan. Dead man on the rooftop, what to do with the corpse? Leave it there? Moriarty's phone is still there, and maybe information on it. Take the phone? Likely. Does he profit from the corpse being found? Not really. If Moriarty's accomplices find out he died, any possible information on that phone would become dead ends quite soon. So the corpse must be hidden, or at least found by the right people. Proven by the fact that nobody ever mentioned dead Jim after the jump. His death isn't public knowledge.
Back to Sherlock: He couldn't have anticipated the death and his time was running out. Sherlock had to jump soon, fake his death, otherwise John would die. If he jumped, though, soon there'd be people checking the rooftop from where he jumped. I guess that he had to call his other "participant" to take care of the corpse before jumping. Again, Mycroft, I guess. Lestrade wouldn't have the power to pull that off. neither would Molly.
From this, I deduct that he had help from Molly and Mycroft.
Why call John while standing up there? Well, he positioned John - out of the sniper's field. Also, probably far enough away to keep him from observing his death too closely. All of this could have been done by text. Sherlock texts, doesn't he? So why call now?
My guess is: he needed to buy time. For the corpse to be removed before he jumped. Texting would make John shout - then people would look up and Sherlock would have had too many eyes on him. The danger of his fake death being detected was too big. Talking over the phone to John probably was already quite a dangerous thing to pull. But it kept him on his position and bought time.
7. "Keep your eyes fixed on me." For Sherlock's trick, John musn't look anywhere else. Why? John couldn't have seen the entire fall, not from his perspective. In my opinion, this is a psychological thing. John then sees what he wants to see. And he stays until he has seen it completely. Stays there during those few seconds which Sherlock probably needed for his trick.
8. The fall; actually we see Sherlock falling but not how he hits the ground. Only that something hits the ground. During his fall, his feet are moving as if he's trying to reach a certain distance from the building. To the car that waited behind the bus? It's quite some ground to cover, well, the fall was deep too. Then there's the matter of the body that hits the groud. It cannot be confirmed from where that "body" fell. The rooftop? Or the car's roof?
The body also hits the ground horizontally, face down actually. Sherlock jumps vertically, with his feet working. It would be more likely for him to "splatter" vertically, then fall backwards due to his feet movement. No expert here, just half-knowledge about gravity. To me, those two seem like different falls.
9. John gets hit by a cyclist; definitely deliberate, the person rams him straight from behind and doesn't stop to ask if he's alright. Also doesn't stop at the corpse's side. The cyclist meant to keep off John - from getting closer to the corpse? From getting into the sniper's view before the sniper got a confirmation of Sherlock's death? I believe in the latter, actually. Even if John had gotten sooner to the body, he wouldn't have gotten more time with the corpse. There were already people there when he arrived. The same people that kept him off a few seconds later. The cyclist thus had to have been informed by somebody about the change of circumstances. Sherlock probably didn't anticipate the snipers. So Sherlock called/texted somebody else, one of his participants. That participant then got in contact with the cyclist.
10. Body on the ground, another lengthy paragraph:
The person on the bench has disappeared - coincidence? I don't think so. All persons rushing to the body are coming from different directions than the bench - except one, and that person is not running towards the corpse but towards the first people approaching the body. Actually, she runs past the corpse - interesting, isn't it? Definitely a participant. Didn't even check if there's still "life" in the body. The first persons at the scene are two "medics", or rather: two persons wearing blue uniforms. Not passengers.
The blood is not there yet when the first people arrive - and when John arrives at the scene, it is concentrated on the head area. That indicates either a prior head injury from which the bleeding occurs or fake blood.
John also checks for blood pressure - reminds me of the small, black ball. He apparently doesn't feel a thing.
When the body is turned over, blood is spread over both of Sherlock's cheeks but we cannot spot where the heavy bleeding is coming from. Under Sherlock there's almost no blood - indicates that it is fake blood. Maybe from the vial that clinkered in the mortuary.
Two of the four people helping to bring him into the mortuary are clothed in business-wear. The blue uniform people didn't keep them away, they were mostly focused on John and one or two of the audience. Business people whose suits remind me of Mycroft's clothes. While I do believe that the homeless network could have helped with distracting John, I don't think they were involved. Too many people knowing about the fake death would be contra-productive. No, I think the cyclist also was one of Mycroft's. This leads to me deducing that Sherlock only involved Molly and Mycroft.
That's it from my side.
The fall, as I guess, happened as such ( background story aside):
Sherlock jumped down, determined to hit "the big car that was behind the bus". Probably there's some sort of material on it that dampens his fall. In those few seconds John was kept at bay by the cyclist, Sherlock rolls of the van, allows himself to hit the ground. Falling from a van still makes a great "thump" noise. Some of his participants kept the first audience at bay while Sherlock spread the blood. Maybe he had hidden the vial in his scarf, thus the concentration on his head area ( though I consider this not as likely, the glass could have cut him - even from the low fall the vial coul have broken). John got through to the corpse as he's a doctor - Sherlock had put the ball there before, so no pulse. John is again pulled away. Four people, two paramedics and two business people (all participants) throw Sherlock on the stretcher, then they hurry him away into the building.
Blood probably is of human nature and from Molly. Van disappeared, corpse is gone within seconds, only thing that remains is that small pool of blood. Only evidence besides the eye witnesses.
Probably not entirely correct, but that's my try.