I'd criticise any story if the only reason a character was female was for muh fehmule empowuhment (love that spelling btw, def gonna steal that), but I don't think this was one of those cases. Almost nothing about her character has anything to do with her being a chick other than it allows her and Finn to force some really awkward romantic moments onto us.
She is a Mary Sue though, I'll grant you that, and not coz she's a looker, but for the reasons you gave. All her struggles happened either before the movie or are inside her own head. Oh, you lost your parents when you were a little kid? Oh, boo hoo, you're young, smart and talented, fit as all hell, and most importantly, you're not this guy.
Everything that happens to her int he movie isn't that awful considering the universe she exists in. Sure she gets chased by stormtrooopers (she was super keen on the whole rebellion idea so she was probably into it) and kidnapped by an emo, but yeah, she handles all that like a pro somehow. I get she's got the force, but even Luke had to drop some rocks and Yoda, and get his ass handed to him before he was able to beat another Sith.
As for the cheesy lines and the way they act, that's just Star Wars, I wouldn't want it any other way.