As far as Rey goes, this is how I see it.
Her flight skills - she didn't fly perfectly at first, I seem to recall her crashing into the ground and hitting things in the beginning. She quickly adapted, and the learning curve was pretty quick, but she wasn't perfect, just good enough.
Her mechanical skills - she had been making a living scavenging off the old Imperial and Rebel ships for years, over that time Im sure you start to get a feel or understanding for how things work. I have a bigger problem in TPM with how Ani can not only build a pod racer, but can build a sophisticated robot lik 3PO.
Her fighting skills - she had been defending herself for quite some time with her pole arm weapon, which isn't a far cry from the type of skill needed for a saber.
Jedi Powers - Well, most seem to believe she is not only force sensitive, but a skywalker who was hidden for her safety. So combined with her fighting experience, something Luke did not have, she managed to best a badly injured Kylo Ren, and honestly, I'm not sure Kylo Ren was that talented a fighter to begin with. So, really she only managed to out force Ren by using telekinisis to acquire the lightsaber.
