Okay, I rewrote my whole damn thing. I think some may have become very attached to the idea that Ren was some sort of badass before the movie. He isn't. The trailers lied or misled us about a lot of things, and I personally think that's fantastic. I love them for that.
Kylo Ren is still a mere padawan. Obviously it is a double entendre when he said, "I know what I have to do, but I don't know if I have the strength to do it," and the clear answer given for which it meant was, "Kill my father." This is one of his trials. That's why the Supreme Leader said he wanted Ren brought to him to "complete his training". In a general sense force-user training, just like in the real world, never really stops. That's why the older more embattled Jedi/Sith tend to be the most powerful, and not the ones with the benefit of youth. But what they refer to as "training", which has a definite finishing point, is the completion of five trials (younglings face three trials to become padawans). The completion of these establishes the point at which a Padawan becomes a Jedi Knight. Clearly Ren was ordered to kill his father as part of his training. I assume it is one of his First Order trials or tests. We don't really know anything about their religion, or if they even consider it a religion like the Jedi/Sith.
He is not a Darth Maul. He is not a Count Dooku. He is sure as hell not a Darth Vader. He's just a scared kid. He's also a Skywalker, the most powerful Jedi family in Galactic history, so the fact that he is so capable isn't difficult to understand. However, like Anakin, the grandfather he worships, he is at his worst when he lacks emotional composure, and especially when he is emotionally conflicted. In the first scene when he captures Poe's blast, he is composed. He only slightly loses composure when his identity is referenced, but he is in full control, and channeling his anger and frustration. Think of Anakin against Dooku #3. After he kills his father he is NOT in the moment. Also, Jedi have been known to be killed by snipers, which is regarded as cheap and dishonorable, and isn't as easy for them to prevent. Chewy is a hawkeye with that crossbow blaster.
Per Rey, the crystals in the lightsabers are special pockets of the force, and like wands in Harry Potter have a special connection to the user. For the Jedi, this was a test, in which they would enter the Jedi caves on Ilum. There they would experience visions. The cave would detect their fears and weaknesses, and test their discipline. They could obtain their crystal by overcoming these spiritual obstacles the cave would erect as a gauntlet to the crystal. Some crystals call to more than one Jedi if they are connected as Anakin/Luke's did to Rey. It is understandable she had more influence over it. Maz commented that what Rey was seeking was "in front of" her, not behind her. Kylo reacted to the news of a "girl" with great anxiety. It's like he had seen her in a Force vision or had the advantage of First Order intelligence. All of this leads me to believe Rey is Luke's daughter. It's perfect. Who else could match his supreme natural talent with the Force? No one. It's also highly plausible that Luke would consider having children a duty to the Galaxy and the Force, and not a violation of his order's beliefs.
Per the Force, you're thinking of it wrong. It's more like a decathlon. Sure, training and skill have great influence over certain events, but there are freaks out there who can walk out and be pretty damn formidable without doing anything. Often, the character of their lives influences their aptitude here. Rey seems no different. She spent her whole life a survivor and an explorer, scavenging, in solitude, and having to maintain her control of herself in an insufferably unjust and brutal society. She has been preparing in many way to tap into the Force her whole life, and so much of the Force is about centering oneself and simply believing.
If you think about it, her defeating Kylo in his state is far less outrageous per our typical understanding of training and wisdom strengthening them versus Luke defeating Vader after a few year's training. He is deeply wounded, and having to expend concentration and focus on merely sustaining himself, likely. A normal human would have died to that blast. These aren't little things. But Kylo is clearly not focused. Finn picking up a lightsaber doesn't give him force powers. A force push that sent Rey flying could kill Finn. He could also probably defeat Rey this way. She's not that honed. He isn't composed.
This is what elevates Star Wars, IMO. You then realize it isn't necessarily just about their mastery of a saber. It begs you to piece together things that don't make sense. You begin to wonder about things: like if Anakin couldn't overcome his subconscious desire to save Luke out of father's love for his son. It was also thoroughly established that Anakin was a more powerful Jedi than Obi-Wan, and better with a saber; he didn't lose to him because he was the weaker Jedi, but simply because he was the lesser Jedi. He couldn't steel his character. Obi-Wan was unshakeable.
I also think Abrams did a brilliant job of showing that, relative to the older masters we've seen fight, we were watching two kids with sticks. These were not the masters like Anakin, Obi-Wan Maul, Windu, Qui-Gonn, Dooku, Yoda, Palpatine, or others. These kids would get carved up by those Jedi. They're going to become much more dangerous and powerful as they develop their discipline.
Man, it sort of killed me that when Han said, "We miss you", he didn't also say, "I love you."