I have read many posts regarding Tobi's identity and whether he really is Obito or somebody controlling Obito, many times Izuna Uchiha's name has been taken and etc. Well, here is my theory:-
We all know that Madara Uchiha respects Hashirama a lot, even though Madara considered him as his foremost enemy. At that time (when Madara and Izuna both had MS and Konoha was formed by Senju and Uchiha clans) it was pretty obvious that there would be a clash between Madara, leader of Uchiha clan and Hashirama, leader of Senju. It is possible, that Madara and Izuna knew at that time that if this clash was to take place, it would be risky business since Madara did not have a sure-shot victory, but neither did Hashirama.
However, the concern over Uchiha's victory over Senju was even more compromised when Madara lost his eyesight by overusing MS. Here, there are two theories put forward by Kishi (he must have just one, but the two are told from different perspectives):
1) Madara forcefully took away Izuna's eyes to get EMS. (as claimed by Itachi)
2) Izuna willigly sacrificed his eyes for the sake of the clan. (as claimed by Tobi)
We are still not sure whether case-1 or 2 is true. Let us assume case 2 is true, since my theory depends on this.
Basically, when Madara lost his eyesight, both's concern regarding their clan's future increased. They knew their chances at beating Senju were slim, especially with Hashirama around. However, that wouldn't be a problem in the future when Hashirama would have been dead. So, they decided to have a 'backup plan' in case Madara was defeated by Hashirama.
1) Izuna gave his eyes to Madara,
2) Madara got EMS,
3) Izuna's death was faked (with Madara's EMS and extremely strong genjutsu like tsukuyomi, it wouldn't have been tough),
4) Madara lost at the Valley of the End but managed to get Hashirama's cells and shortly after awakening rinnegan Madara died,
5) Izuna got his hands on them cells and rinnegan, developed Zetsu, became first tobi by using Madara's EMS and Rinnegan to do all that stuff that made Kisame believe he is madara, blah blah blah.
6) Obito gets crushed under a pile of rocks, gives one sharingan to Kakashi but is saved by Izuna 'Tobi'.
7) Izuna teaches him everything, including how to gain Mangekyou Sharingan and uses Hashirama's cells to heal him (similar to Zetsu's sticky white material). Izuna is also brain-washing Obito here, but is not very successful.
NOTE: Here, Obito might have had a major growth spurt because of Hashirama's cells, hence could be physically tall enough to be the man who fought Minato.
8) Izuna finds Nagato, gives him rinnegan.
9) RIN DIES, maybe providing the emotional trauma needed for MS (he couldn't save Rin because of some reason and it is known he had strong emotional attachment towards Rin. this may also be the reason why Obito resents Kakashi, as Kakashi had promised that he would take care of Rin). He has obtained the current 'Tobi' mindset and decides to end the misery of the world, blah blah blah.
10) Izuna is satisfied that 'Tobi' will carry on his plan, gives all his chakra/powers/knowledge/legacy/(whatever-you-think-is-cool-to-pass-on) to 'Tobi' and handles him the responsibility and leaves the world. R.I.P. Izuna. Maybe, he might have just put his soul into Obito and he is somewhere in Obito's conscious/sub-conscious, kinda like when Naruto meets Kurama in his sub-conscious.
11) Attack on Konoha by 'Tobi', who is both Izuna and Obito in one body (Obito a vessel for Izuna's and his own soul???). Thus, Kurama noticed the eyes of 'Tobi' as that of Madara (Izuna took Madara's EMS, they both look like twins) and 'Tobi' also had Obito's MS, allowing him to use Kamui while fighting Minato.
12) Naruto gets Kurama sealed in him, Uchiha tragedy, Sasuke's quest for revenge...
13) Tobi revealed.
I also found it customary to answer all those questions.
How come he survived?
- Izuna saved him.
Was it the head injury which made him go Tobi?
- No. It was partly brain-washing from Izuna, but mainly Rin's death.
How come he thought he had a claim over Nagato's eye?
-Izuna gave the rinnegan to Nagato, hence he did actually have a claim.
When did he had that growth spurt and MS awakenned?
-Growth spurt-> Hashirama's cells.
MS-> Rin's death.
Is it only the body of Obito?
- Nah. Here, I would also like to explain another part of my theory. Suppose Izuna only leaves his powers with Obito. Even then, the theory would remain true to the points. Also, look at Tobi here not as a name, but as a title, like Hokage. Kishi doesn't want to name a person Tobi, he wants to name the idea Tobi. That is why we have so many so-called 'loopholes' which is actually a way of Kishi's telling us that Tobi does not refer to one man, but one idea, and could be actually a combination of many different people who thought the same way and had the same goal. Just a thought.