Regarding Rey “downloading” lightsaber skills to defeat Kylo, I see what you’re saying but I look at it like this: A big part of the Force is that by “letting go”, you let the Force partially guide your actions. This is how the Force is described in the OT. So when Rey closed her eyes, she let go of her doubts and her fears, and let the Force flow through her and guide her actions. I think it carries a strong message of believing in yourself to overcome the challenges you face.
I think by that point in the battle, Kylo was afraid, injured and unbalanced, only going off his learned skills, which is no match to the power and reflexes the Force can give you, which Rey had at that moment.
Also with the Jakku chase, the First Order had orders to capture the droid, so they might have been trying to disable the ship rather than simply destroy it, which might’ve made their job a little harder.
The Jakku chase still seems a bit iffy-it’s been a while since I saw it-but what you said makes sense about Rey and the Force in her first showdown with Kylo. And there’s precedent with Luke in A New Hope. Obi-Wan just tells Luke to use the Force, and he’s able to blindly block the little floating sphere’s blasts. Same with him suddenly using the Force to target the Death Star’s weak spot instead of actual onscreen display schematics.
Plus, she already has experience fighting with a staff, so that, combined with allowing the Force to guide her actions, makes the scene work in hindsight.