The ship seemed to be both alive and machine. Almost the cylons adaptation of the human clones in space. If it was truely and only biological, wouldn't the death and then removal of the brain have shut off the systems and all it's uses.
So for me I can fudge around and make a plausible reason she could have had a working ship.
Tearing cloth off her suit and pushing it into the whole... not plausibe. Yes, she could have done a better patch job, but with what? Not to mention why show so much about the cloth being shoved in if she just had to redo it with a better patch job?
For her flying.... she's great, the best, and relies on instinct. She knows apollos flying style and tactics, and she only did one or two complex manuvers. Mostly she just seemed to weave back and forth heading as quickly as possible for galactica.
The paint.... maybe some of the other parts she ripped out of the ship had orange/yellow goo on it. It did make it better that we didn't see her painting the ship before hand. It made for a better surprise and confusion about what she was saying and her reasoning until she flipped the ship.