Batman needs to chill

Being able to swing things at crippled dudes isn't hard. She was clumsy with it until she summoned the Force.

It is when the blade has no weight to it at all. If you were used to a balanced weapon like a staff, you'd overswing to fuck. Not be able to block another lightsaber as it comes at you.

And she did some overswinging parries that weren't particularly effective against Ren's onslaught, but probably would have worked nicely with a staff. She also tried to poke with just about every attack series as though she were lunging with a spear or a staff.

And should have not been able to fend Kylo off, never mind beat him.

She didn't fend Kylo off. She got beat down and pushed back by a superior yet crippled opponent, and only beat him when she summoned the Force and let it guide her movements, just as she had when she pulled off that otherwise impossible maneuver in the Falcon that let Finn shoot a moving target with a broken turret. It was foreshadowed.

Luke probably could have done the same thing with his minimal training on Bespin, against a far-more-powerful-than-Ren Vader, but he was too distracted by his own urge to save his friends and Vader keeping him off balance with Dun Moch tactics. Rey shut out all her distractions and let the Force flow through her, just as Luke did when he made that otherwise impossible shot to destroy the Death Star.

And there's another thing- she shouldn't have at all been able to summon up the force like she did. She's not a fucking Jedi, she hasn't had the training to properly clear the mind to use the light side of the force, ESPECIALLY considering she in no way was in a peaceful environment. She was in the middle of a battle for her life and she was just like "lol it chill".
There's a reason that Jedi train years for that kind of thing- a completely calm mind, like the sort needed to let the force guide your movements, is not a thing that comes naturally.

The thing is, because the EU has been retconned, there's nothing to say people who have a connection with the force can't accidentally have it affect them like Harry Potter letting the snake out of the tank or setting a hedge on fire

There's more out there in the galaxy than Sith and Jedi, and they get by just fine without huge temples, highly organized training, or formalized doctrines. There's shamans of primitive tribes who use the force to heal wounds, cure diseases, and see the future, stuff even Jedi often find tough to do.

Rey lived a sparse, rote, very zen existence while waiting patiently for her parents. Instead of looking to the horizon for adventure and glory, she waited. She was basically a Jedi already. And, she only ever did what Luke had done several times during A New Hope, with equally non-existent training, let the Force flow through you. It's the most basic concept of non-Dark Side Force use, so of course it came easily to her. People do it all the time without even realizing they're Force-sensitive, just thinking they're lucky or especially skilled.

You're right on the first bit- these kinds of things canonically exist, there's no question about it. They also tend to do these things in calm environments where they can actually use the light side of the force.
Ray was in a heated battle, and had just before been pretty emotionally controlled. She certainly should not have been able to almost instantly calm her mind and let the force flow through her. And those tribals that use the force? They train with it, still. They don't go through the jedi training or sith training, but they go through their own.

As for luke doing the same thing, he did it with the spiritual guidance of Obi-Wan Kenobi, as well as already knowing exactly what had to happen (I'm assuming that you're talking about the destruction of the death star. It was already known where the bomb had to go). He also wasn't locked in melee combat with a trained opponent- he was focusing on a specific point that he knew had to be destroyed.

Maybe she was crazy angry, and her becoming powerful could hint at a dark future. Just spitballing, but I don't think it could be outside the realm of possibility.

That would be damned cool if that were the case
I doubt it's gonna go that way, but it would be an amazing twist

And yet, as I mentioned earlier, untrained people use the Force all the time, doing the same things she did, without even realizing they're using the Force. Rey knows the Force exists, knows what Jedi are and what they can do, received a Force vision that quite likely imparted plenty of knowledge into her. All of that crystallized in one moment where she let go, and then proceeded to use the most primal, basic implementation of the Force that anybody with the potential can do. Anakin was channeling the Force and doing ridiculous things at 8 years-old, to the point where even his mother realized he had to have special powers. Shit like what Rey did has been in the canon for over a decade, such that even Star Wars tabletop RPGs create mechanics to emulate it. The Force lets you do crazy, impossible shit, whether you have training or not. Luke couldn't lift an X-Wing, even with a tranquil environment, because he didn't believe he could. Rey defeated a wounded Kylo Ren because she let go of her doubt.

Outside of Anakin (who can be discounted because he literally prophesied to be immensely powerful, in order to bring balance to the force. He's essentially a force sock puppet) when have we seen untrained force-sensitive beings use the force in controlled ways? What she did wasn't a primal thing, it was becoming one with the force to become an incredible fighter.
Luke couldn't lift an x-wing in a tranquil environment because he wasn't balanced, and thus neither side of the force quite called to him.

And Rey knowing what Jedi are and what they can do is bullshit. She didn't even believe in them before Han told her about them.