Something that I do want to comment on is how I don’t see his character as a villain. He’s maybe angry at the world and struggling with emotions and can you really blame him for his personal confusions and anger?
Luke’s moment of weakness was an altering one as he contemplated killing Ren- someone who very likely saw Luke as a legend and was let down completely by Luke attempting to sneak and take his life. His retaliation against Luke is somewhat understandable, though perhaps Snoke whispering things in his ear really turned up his anger towards Luke. I'm sure, prior to TFA, Snoke was telling Kylo everything he wanted to hear until he put Kylo to the task of murdering his loved ones to complete his training and decent to the dark side (which we all know was done with great reluctance as he told his own father to help him in that situation and doesn't fire upon Leia).
By the end of TLJ, Kylo is ready to part ways with both Luke and Snoke- both whom let him down is great ways. One theme that TLJ mentioned is how imperfect the Jedi truly are but they’re still glorified and thought of as legends. Luke was well aware of this, especially after failing Ben Solo and being the final push Ben needed into the dark side. Because of this- Ren and Luke weren’t wanting completely different things as they both wanted to re-write the ways of the Force. The difference between the two is the anger that Kylo holds towards Luke, while Luke feels responsible/guilt. This movie also shows that, when it comes to the light side and dark side, it isn't so black and white- there are gray areas.
After Kylo's fit against Luke’s projection, we are shown a defeated Kylo as he picks up his dad’s gold dice. When the dice disappear in his hand, he grips his hand almost as though he’s trying to hold onto the memory. To me this scene didn't depict an angry, evil and vengeful person, but rather someone who feels extreme sadness and loneliness. Even when he and Rey were staring back at one another's projections, his expression is pure sadness. To end this scene they show him hanging his head- which makes me believe that, in this moment, the audience wasn't looking at Kylo but rather Ben Solo. With that ending, it's not a question of if he turns but rather when he will turn in the 3rd movie. I speculate there will be some type of mutiny against Kylo from General Hux and his men at some point- maybe that's when Ren will turn?
Something else I want to mention is how this movie proves that the Jedi can't see the future but rather they see glimses of what will happen. Rey says she sees that Ren will turn while Ren claims he sees Rey will convert to the dark side. . So far though Snoke, Luke, Rey and Ren's visions haven't been wrong in some regards so it makes me wonder to what extent will Rey go to the dark side?