They show at the start of the film that she's a scavenger, she literally lives or dies based on what she's able to bring back to trade. It makes sense that she would realize early on in life that a working part will fetch more than a broken part, so knowing how to fix and/or break bits of technology isn't stretching my belief too far.

I agree that it's feasible, but the part where she knows how to work the parts of the First Order ship is a bit of a stretch in my mind. Even with the First Order technology being built on the foundations of the Empire (whose ships she was shown scavenging), I don't think it would have been similar enough to know how it worked so quickly. I guess it's feasible though, so I'll let it slide.

She's living in a rough situation on her own, they show her fighting with her staff before she leaves her home planet. To me her lightsaber fighting style didn't look like any other jedi from the previous movies, it looked like how she fought with her staff.

I think showing her with some fighting ability is apt, but the outcome of the final fight, despite the circumstances, was unrealistic to me. (Spoilers)Even with Kylo seriously wounded, he's pretty much depicted as a god in power throughout the movie. She should be struggling for her life, but instead she makes Kylo look like a child. Especially true with the "force pull battle" part. Kylo is one of the most powerful force users in the galaxy, no way he should lose that force battle with this girl who didn't even know what the force was 20 minutes ago. I think the scene would have been better depicted as her desperately defending against blows from Kylo before being saved by the ground splitting, not her completely outmatching him and Kylo being the one who is saved by the canyon.

Anyway, it's only the first new movie. Anakin was a bit of a Mary Sue in Phantom Menace as well, and wasn't really given flaws until the next episode. Hopefully they round Rey out a bit as well in future films.