Fixing Rey
Okay I usually focus on how much I despise the character. So for this thread i am going to suggest what I think would fix the character and still allow her to do nearly everything she does in TFA itself, most of this is going to involve her 'introduction' scene and it would be vastly different but for the rest of the film post meeting Finn the story could be exaclty the same including her being dropped off on Jakuu as a child and no need for her to have a force training background that was wiped out.
First, show her doing more than being a loner and only scavenging. Instead have her doing things like show her socializing in jobs as a pilot in between camps with scavenged goods. She is both socially 'normal' and a great pilot so they should do things to show why she is like that. Maybe show her have a few friends while on piloting jobs for Unkaar and quick little social exchanges. Like she gets back from scavenging and Unkaar only gives her 1/4 portion and says 'if you want the rest fly the parts to "Y" camp and collect payment'. Then show her doing that instead of the wasted time with a 'pilots' helmet eating by herself and staring at an old lady 'dreading' her own future. Show that she is too busy to dread anything and that is why she doesn't leave on her own. Too busy to think about leaving would make more sense than what we got, of course it would make her less sympathetic to millennials.
Next, show her doing a fighting pit for money(food). Show that she willing participates and is competent in an fighting arena; maybe even with multiple weapons. This would suggest she has being it for some time and would make her later battle prowess not only acceptable but cool. Again this would likely make her less of a sympathetic character. What is the key part of the sympathetic - pathetic.
Third, show her having some exchanges with the Church of the force or suggest she knew them and was sad to hear they were all killed. Maybe Finn could tell her that is where he was escaping from and she is saddened by this and he gets a chance to consul her, which would humanize her and give their relationship and chance to develop naturally. Also it would help making Finn look less pathetic. Also it would explain her ability to pick up the force if she had heard more stories about it previously. This does not even need to be fixed elsewhere in the film because they could suggest that though she was friends with the church of the force she did not actually believe them until Han confirms it's the truth. This would totally fix her rapid force learning. Because she would already be aware of the powers and just need to believe it and 'try' it.
Literally nothing else in the film would need to be changed. She could pilot the falcon, escape with Finn, Kick ass with a lightsaber and staff (fighting pits shows her using both), develope force abilities unusually rapidly, have well adjusted social skills, etc. I mean you could even have her fighting a Wookie in the fighting pits and talking with it showing they were rivals or something, so when she speaks to Chewie it makes sense that she would know Wookie. Story people, story is more important than lazily contrived sympathetic imagery (like the wasted marking on the wall scene). If they wanted to include those they could have. I would have been fine with the film being 10 minutes longer if they had actually fleshed out the character. And I would have been less annoyed with other lazy parts of the film because she would have been such an interesting character.
Now, even though I give fixes that would undoubtedly make her character even more 'bad ass' queue the accusations of sexism and of me having 'fragile male ego'.