How is it possible for Obito to have his right Sharingan intact? When we see the old Madara talking to Obito after he was found, we can see that his right part of the body is destroyed and replaced with that artificial, Hashirama cells included "body", and we can also see that his face is in a pretty bad shape, too, but he's got his right Sharingan. How it happened, that his right eye came out harmless after that incident?
There's no actual reason given. It was stated that "Madara managed to save his eye".

It was also half-implied that his Mangekyo was awakened for a brief moment and allowed him to slip through the rocks (Madara said something similar to that when Obito awoke for the first time).