Here's my theory on how he survived and what he did afterwards:
Well, though i didn't want to believe it myself, it is clear that Obito has "survived" in both body and mind.
Obito Clearly said that the reason he has done this is because Kakashi let Rin die. Whether Madara also had any impact upon him is unknown, but what is known is that Madara knew Obito. This confirms that Madara was alive atleast long enough to know Obito.
Obito survived like this:
In order for Obito to have survived he would have to have either instant regeneration/revival(Which can only be obtained by either edo tensei(which he clearly isn't), Hashirama's and Tsunade's ability to instantly regenerate, or the Naraka path)
It is known that Madara had the rinnegan before his death, with the rinnegan he has the ability to resurrect someone, anyone who is recently dead with the naraka path. This would restore his crushed Sharingan and the rest of his body.
Madara then takes Obito under his wing for long enough time to transfer knowledge and train him, this happens between the time of Obito's death and the Tobi's attack against Konoha with the ninetails.(Sometime during this time Rin dies, enraging Obito, Madara dies after Rin's death seeing as how he knows about the plan).
Also it may have been possible to transfer Madaras knowledge using the human path to Obito.
This causes him to do the following:
Obito now knowing that the seal for a bijuu is weakest when its host is giving birth(due to knowledge gained by Madara), he attacks Kushina and releases the Kyuubi and controls him(the ability to control the Kyuubi was taught to him by Madara). Obito then loses to Minato which shows his left arm(which wasn't crushed by the rock) is made of zetsu stuff, possibly lost in a training accident or added to his body to make it more repairable after madara's death(or allow use of izanagi).
After Obito's failure he plans, schemes, trains, makes more zetsu's, and eventually kills the mizukage and takes control of that village, allowing time for his hair to grow out so people would believe he is Madara Uchiha. Around this time he also helped Itachi in the killing of the Uchiha clan. Obito manipulates Nagato and essentially becomes the Akatsuki's leader, they gain members and become powerful enough to retrieve the bijuu and seal them in Gedo meza. They inevitabally capture 7 bijuu after many akatsuki die and tobi is then revealed to be the one pulling the strings to those of konoha. Tobi captures pieces of the eight and nine tails and now is attempting to summon the Juubi. His identity is revealed in the fight. Madara shows up and affirms tobi is indeed Obito.
Some people may say, well how did Obito grow such much in such a little time? Well i don't know about you but kakashi and Gai sure look about as tall as they are now meaning Obito easily could have grown the same amount in such a short amount of time(Possibly more since we don't know whether or not his dimension slows down time).
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Also some people may say that how could Obito have been the tobi controlling the mizukage? Obito had to have been the one controlling the mizukage since Kisame recognized Tobi's face when shown to him and calls him the mizukage. link to the chapter below.
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