He did. He said he "slipped away or through" the rock, which is why he wasn't completely crushed and survived.
No. Obito was indeed completely crushed by the rock. After the cave collapsed, his sharingan temporarily activated MS and he fell through the floor, along with the rock. He fell into the pathway leading to Madara's hideout. This is why Madara stated Zetsu found him near the rock and that he must have slipped through.
Which makes no sense to me. How would this be possible if he didn't unlock his MS ability until Rin died which happened after Madara saved him?
It was temporarily activated in the moment of crisis.
Nah, I think he managed to stay alive thanks to his will power. Obito has proven to have a will as strong as Ashura's incarnates, he most likely kept himself alive based on pure will like Kimimaro and Itachi
Probably this.
To reiterate, Obito was indeed crushed by the rock. The time he spent talking to Kakashi and Rin, not to mention the time it took to transfer his left eye, he was dying during that time. After the cave collapsed, his MS temporarily activated and he phased through the ground, taking a rock with him. That is how he ended up in the pathway to Madara's lair and that's how Zetsu found him.
Afterward, his body was treated with Zetsu cells. His head was crushed to a degree but not fully, hence how he kept his right eye intact.