1) "He has broken up with her for 7 years" that means that every day for the past 7 years he talks to her and says "we're over. I'm done. I'm moving on. I've met someone else. It's not you, it's me. We need to see other people. I'm leaving this relationship." And she either refuses to believe him and claims to still be his girlfriend or he takes her back later that night and then goes through the whole thing the next morning. (There are people like that). My guess though, is you mean to say "They broke up seven years ago." 2)"She hasn't gotten past the break up" (and no surprise, since he's been breaking up with her daily for 7 years :) )

For me I would say that "He has broken" is only for use in the present tense, like for example: He has broken my heart. If I was to re-write this sentence in past tense I would write it like this: He had broken up with her 7 years ago. And the second one, seems correct, but the word "gotten" isn't used much in British English, but IS used more in North American English. In British English I think it would be correct to say: She hasn't got passed the breakup, or She hasn't recovered from the break up.

To add onto Marcus for the second question, in Canada, it is common to say "she hasn't gotten OVER the break up".