Kylo Ren was always obsessed with his grandfather. He didn't learn he was the grandson of Darth Vader until he was a teenager, when a recording from Bail Organa - intended to be a private message for Leia - was shared with the entire galaxy.
Ben Solo only discovered the truth about his grandfather when Casterfo revealed it to the Senate, which means Leia had lied to him for almost 20 years. This discovery is what led Kylo Ren to finish what Darth Vader started and began his obsession with following in his grandfather's footsteps.
Kylo chose to idolize his grandfather for what he once was, viewing him as Darth Vader and not Anakin Skywalker. However, Vader's turn reminded Kylo that he had the same weakness within himself.
On one hand, Kylo Ren saw himself as the heir apparent to Darth Vader, someone to look up to and emulate. On the other hand, he did see his weakness and was told that he was a warning. Something to look at and see as a problem. Very much a paradox of the dark side.
He saw her as a useful tool for his rise to power. He was intrigued by the mystery surrounding her. He wanted closure for his defeat at her hands. He had a genuine emotional connection to her.
When Rey went to meet him on the Supremacy in an attempt to convince him to turn to the light, Snoke reveals that he had manipulated their bond to lead Rey into a trap and starts to torture her in front of Ren. This infuriates Kylo, who at this point had developed strong feelings for Rey.
Summary. Rey gained knowledge and skills through her connection with Kylo Ren, allowing her to tap into his training and skills. Kylo Ren was wounded by Chewbacca's bowcaster, which he believed inhibited his ability to defeat Rey.
Though initially trained as a Jedi by his uncle Luke Skywalker, Ben was seduced to the dark side of the Force by Supreme Leader Snoke, and aspires to be as powerful as his grandfather, the Sith Lord Darth Vader / Anakin Skywalker.
During the Imperial Era, a human female nurse served the Galactic Empire on board the Death Star under the supervision of a doctor. They both served the Sith Lord Darth Vader as his personal medical caretakers. The nurse became obsessed and psychotically in love with the Dark Lord of the Sith.
Kylo Ren wanted to be the next Darth Vader, fundamentally misunderstanding his grandfather. Another key reason why Kylo would never be the next Vader was that Kylo was a Knight of Ren, not a Sith. While both religions used the dark side, and red-bladed lightsabers, the two had different philosophies.
Not only did Ben care little for the Jedi, he also viewed Luke as the person keeping him away from his parents. And the strict rules of the Order only made matters worse, as Ben felt they limited his potential, and forced him to forgo attachments.
For the first time in all his life, Darth Vader sees a Jedi act the way he was always told Jedis should act, and seeing his son become the ideal of what the Jedi Order claimed to be made Vader not only love his child, but greatly respect him.
The lightsaber Kylo Ren longed for as his birthright was instead claimed by Rey on Starkiller Base. You need a teacher! I can show you the ways of the Force!" After incapacitating Finn, Ren attempted to summon the lightsaber to him, regarding it as his own property due to its history.
Kylo Ren's "unstable" lightsaber was designed to kill. Knowing Makashi, he would become a much more dangerous foe as he could disarm and eliminate his opponents far quicker without the need to endure a long, intense fight. Sadly, he didn't learn Form II as there was no one around to teach him during his younger days.
The helmet was designed to look sinister; as a Knight of Ren, Ren was part of an enclave of dark side warriors who wore masks to induce fear in their prey. Ren's helmet was a symbolic reminder of his lineage as Darth Vader's grandson, serving no practical use in his life.
Kenobi's hesitance to fight Vader, and his fear of this despite beating Anakin before, all comes from Kenobi's intense guilt that has been building over his 10 years in hiding.
Anakin and Padmé met when Anakin was still just a young boy in Star Wars: Episode I – The Phantom Menace. Though he was already infatuated with her then, it was a boyish crush — one that Padmé could not reciprocate at the time.
It was the fact that Luke was his son that caused turmoil within Vader. It was his love for his son that caused his loyalty to Palpatine and the Dark Side to falter. If Vader didn't know who Luke was he would have been just another force sensitive person to be trained to serve Palpatine like an Inquisitor or be killed.
But this is actually a very sad reason because it actually had the opposite effect, and he deeply regretted his decision to kill his father and it haunted him for the rest of the trilogy. Also, Han was telling him that Snoke was using him, but one of the reasons he killed him was to impress Snoke.
While they may not have had romantic love for each other, they became close enough that Rey would miss him after his death. The kiss at the end of The Rise of Skywalker was a goodbye to a friend who would be dearly missed.
Their battle was interrupted when Leia used the last of her strength to reach her son in the Force. While Kylo was distracted, Rey ran him through with his own lightsaber, leaving him mortally wounded.
Kylo lost to Rey in TFA because he was heavily wounded and was holding back against her due to Snoke's request that he bring her back to him alive. He is also stated by Palpatine in the Secrets of the Sith book to be “equally as powerful as a real Sith despite not being one”.
