Questions:
1. What did Ras do to be sent to the pit? Who sent him there, and who was in charge of the pit? And why did he not go, but his pregnant wife?
He fell in love and married the daughter of the local lord. The lord sent him there, it was his prison. Tas did go, but Talia's mother freed Ras by taking his place in the prison.
2. Why was Bane so attached to Talia in the prison? Why was he the protector?
He valued her innocence. The prison doctor forgot to lock the cell one night and she and her mother was attacked. Bane was her friend who rescued her.
3. Why did the prisoners attack Talia (who was just a little boy looking child) and Bane?
Presumably because they hated her father for imprisoning them. They attacked Bane because Bane rescued Talia.
4. If Talia/Bane's end game was to destroy Gotham with the nuke, why not just detonate the trigger earlier? And if they couldn't have, where in the movie do we learn they couldn't?
Talia mentions something about a slow revenge being the most painful. Bane says that he wanted to give the Gotham people hope, so they would fight each other for survival.
5. Why did Bane say he was apart of the League of Shadows, rather that he WAS the League of Shadows, when he was actually exiled by them?
He was exiled by Ras, not the League of Shadows. He and Talia are both a part of it, but Talia forgave her father after he died.
6. I feel like I am missing the whole point of Bruce escaping the pit. What was the meaning, both literal and underlying, of not using the rope?
To escape without fear. That the whole point of falling was to pick yourself up.
7. In the end, are the pearls with the tracker in the Batcave to lead JGL, or with Bruce to lead Alfred?
The pearls were with Bruce and Selina. It isn't implied they lead Alfred there, because he mentions that he visits the cafe in Florance every year near the beginning of the movie. It isn't a far-fetched theory though.