I don't know if you're content just hating on the movie or if you actually want answers to what you posted. however, there are explanations to these things.
It's not that she knew the Falcon better... but she just understood how a vast variety of ships work in general. That was her trade... & her survival depended on it. Plus, that's all she had to do for all those years.
I can't really say it any better than Rey's Canon page on wookiepedia
http://starwars.wikia.com/wiki/Rey
Rey also had a computer display from an old
BTL-A4 Y-wing assault starfighter/bomber that she used to learn alien languages, study the schematics of Republic and Imperial starships, and run
flight simulations in order to hone her skills as a
pilot. Her ability to understand alien languages, including the
binary language of
droids, helped her when off-worlders came to Niima Outpost. Two such off-worlders were
Wookiees, who regaled her with the stories of the famed Wookiee
smuggler-turned-Rebel fighter
Chewbacca. She learned of Chewbacca's exploits, as well as those of his friend and fellow smuggler
Han Solo. Studying schematics to learn how ships worked was also an important part of her survival on Jakku. She recognized almost all of the Republic and Imperial vessels that could be found in the Graveyard, including what roles they played in combat, the types of weapons they were armed with, their models and classes, and how many crew members each one had. She learned this not just through studying schematics on her computer, but also by climbing through and exploring the ships and tinkering with their systems. This let her know what each part was, what it could do, whether it worked, and, most importantly, whether it would carry any value in Niima Outpost
Kylo pretty much taught her how to enter people's minds when he was probing her & she realized that she could also recognize his thoughts. It actually took her a few tries to get it right, but its the same technique learned while in Kylo's mind. She just enhanced it from reading to inserting thoughts... similar to the Jedi stories she had heard. I don't find it hard to believe at all.
Rey was well known on Jakku for her staff fighting ability, & no one f*cked with her accept for visitors who hadn't heard of her abilities. She was elite... & its not like Luke was really invested in the fight... & he hasn't been fighting for years so he also had ring rust.
I personally don't find it that hard to believe that her abilities as an elite staff fighter can transfer to the sword.
Kylo was the apprentice of what we are assuming is a Sith (not a sith himself)... but to your point, Kylo was trained in Light Saber battles by Luke from an early age & likely further by Snoke.
As mentioned in my previous post... Kylo was trying to recruit her, not kill her. She got a few good licks in but it's not like he was trying to kill her.