Every time I advance a level I get a notification up top saying so-and-so is likely to escape or so-and-so has escaped. I believe that has something to do with the summit, but when I capture an NPC and go to the summit there's nobody there. Once I get the notification that somebody has escaped and I go back to the summit, then I see the NPC that I previously captured is running amok and I have to fight them again. 

So My question is: What do I do with NPC's that I've captured and what is the point of the summit?

You have to restrain them using the restraint button in the collection.

Or you can just release them for a reduced rep penalty.

An “auto restraint” system is in the works but Ive been drowning in bugfixing lately to actually work on it