My post covers several topics so I created a new post. Sorry for inconvenience and sorry that it is too long!
I am grad to hear your opinions.

My theory covers:
What is the final problem?
Why did Moriarty kill himself?
Why not Molly?
Relationship between Moriarty and Carl Powers (who is Moriary?)

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The Final Problem: 1) Who is Moriarty's pressure point?
2) Who is Moriarty?
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Remember the following conversation at 221B between JM (Jim Moriarty) and SH (Sherlock Holmes).

Moriarty:Â Every hotel bedroom has a personalized TV screen. And every person has their pressure point, someone that they want to protect from harm. Easy peasy.
Sherlock:Â So how are you going to do it? Burn me?
Moriarty:Â Oh, that's the problem. The final problem. Have you worked out what it is yet? What's the final problem? I did tell you. But did you listen?

Most naturally, the final problem is how to do with the competitor's pressure point. Moriarty said "every person". Then logically, Moriarty should have "the person he wants to protect". Answer to this will lead to "who is Moriarty?, worth the final problem. (Sherlock said  "what are you?" after "IOU, glycerin molecule". I think this is "what are you, Moriarty?")

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Answer to 2): Dead classmate of Carl Powers
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In the "Great Game":

John: Anything on the Carl Powers case?
Sherlock: Nothing. All the living classmates check out spotless, no connection.
John: Maybe the killer was older than Carl?
Sherlock: The thought had occurred.

Sherlock said he had checked all the living classmates including senior (or perhaps junior). This implies that there are dead classmate(s) and he did not check them.

Moriarty's first crime is "Carl Powers Murder" and the second may be to fake the death of himself.

Nobody knows who Moriarty is.
He can be anybody, Jim Moriarty, a consultant criminal, Jim from IT, Richard Brook, an actor... But this means he is not anybody. Remember that he uses "Anonymous" as his name on the John's blog.Â

As Moriarty did based on information obtained from Mycroft (according to John supposition), to reveal the Moriarty's identity must be Sherlock's final problem.

If Carl were alive, he would be 32 in 2010.
There might be one or more dead classmates but by excluding girl(s) and those who died grown up (such people can be identified by their photos) the target can be easily limited.

Yes, Moriarty was "staying alive"! On the rooftop he himself answered to the question! "Final promlem-- staying alive!
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Answer to the final problem 1): Molly
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What is the our-of-character behavior?: That Sherlock said "you" not "your help"
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By the process of exclusion, the answer to the final problem is Molly, the only person whom Sherlock contacted. And I have another reason.
Please remember the following conversation at Bart's Hospital.

Molly:Â What do you need?
Sherlock:Â You

It is too romantic and not precise for Sherlock.
If he means "preparation for fake suicide", he should say "your help".
He prefers exact expressions and is not a romantic person.
I think this is an out-of-character behavior.
So I think Sherlock meant that he exactly needed "Molly".

After that, he sent a text:

Come and play. Bart's Hospital rooftop. SH
PS. Got something of yours you might want back.

Conversation at rooftop.

Moriarty: What? What is it? What did I miss?
Sherlock: You're not going to do it? So the killers can be called off, then, there's a recall code or word or a number. I don't have to die...if I've got you.

Yes, Sherlock had got something, the pressure point of Moriarty.
So Moriarty had to recall the order to protect it. This means Moriarty's loosing the game.
But he killed himself, which left Sherlock only two choices:
1) to fall, or
2) not to fall, which will result in his friends' death.

Of course Moriarty knew that Sharlok would choose 1).
In this case, the game is draw. So he killed himself.

So Moriarty's pressure point (the person who Moriarty wants to protect) should be Molly, and information she has about him. I suppose she is his sister. Sherlock might have found the name of Molly as a family of the dead classmate.

Sir Arthur Conan Doyle's classical Sherlock Holmes says that Moriarty has two brothers. Then Molly can be one of them.

And this is a reason why Sherlock thought Moriarty must have excluded Molly from the target. (It should be noted that Sherlock did identify the target. So the reason that Moriarty might underestimate Molly is not correct.)

My further assumption is that Molly and Moriarty are a daughter and a son of the cabbie in the Study in Pink.

Their family names are similar.
Molly Hooper
Jeff Hope (cabbie)

Jeff seems to be around 60. So his children might be around 30.
According to the Molly's blog, she is 31.
She said her father is dead.

Children in the cabbie's photo a little look like Molly and Moriarty.
I admit there is a leap of logic and there are other possibilities.
Â
I conclude that Molly was not involved in the fake suicide of Sherlock simply because she was not asked for. This explains why she was referred in Sherlock's note.
If she had helped his fake suicide, she must have known that Sherlock pretended to be a fraud. (The reason why Sherlock pretended so is not to tell the true reason, to die for friends. If no reason, John must think "why Sherlock killed himself?")
Mycroft might have helped his brother's fake death by himself as described in the classical Sherlock Holmes.Â

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I O U: Â Not clear
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Assumption 1): Name or code of the second case (fake death) of little "Moriarty"
I haven't yet cleared what IOU means, but I think it relates to the fake death of little Moriarty, since Molly reacted to IOU very much and repeated it twice.
Besides Sherlock pays a much attention not to tell John about IOU.
After he muttered IOU at the laboratory, he confirmed that John had not listened to him.
He might think IOU is anything dangerous. He tends to protect John from danger. He did not talk about the enemies in Blind Banker (both at 221B and at Soolin's flat). He sent a message on his blog to Moriarty to meet him at the pool without John as well as the last roof top meeting.


Assumption 2):Â I Or You
Moriarty said "IOU a fall"

This means Either of us, the looser, shall fall.
This is a variant of a "You-or-I-will-die Game" in the Study in pink.
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Weak points:
My theory cannot explain:
1) what the hidden camera is and why Sherlock did not turn off it.
2) why the little girl screamed.
3) why the scene after Sherlock met Molly and before he sent a text to Moriarty is inserted. If he had got the answer, he need not be so irritated.

Thanks for reading my theory!