if it was her decision, likely not. if it was mine, it would really depend on the situation. I've never dated or been in a relationship, but I have ended friendships, and never spoke to them again, so I don't care if I lose people, once I am done with them, I'm usually done
Depends on the reason, but generally speaking, no.
Lets say she needed to focus on her studies ( medical school etc ) and she had absolutely no time for a relationship so she ended it for that reason. But we were great together. Then I'd probably take her back.
But she left me for something silly or I didn't like her character then I wouldn't take her back.