I don’t know how I can state it more clear. It was pretty evident to me that Kylo was breaking down and having an identity crisis, just about sobbing to his father. Unless you are arguing that he was faking in order to kill Han, I think it’s objective fact that Kylo was caught in a moment of emotional weakness.
No, not faking it. I think it was obvious that the audience was meant to initially think that he was close to abandoning the dark side, and going back home with his daddy, but afterwards it becomes evident that what he wanted was the strength to kill Han and therefore abandon the light entirely. He is conflicted, certainly. He confides this to Vader’s mask earlier in the film, saying he feels the pull to the light. He also tells Han he is being “torn apart”, and that he wants to “be free of this pain”. And “I know what I have to do, but I don’t know if I have the strength to do it”.
Well he does do it. He overcomes the light in him. His dark ambitions win over the love he has for his family. The guy is clearly in turmoil over what he feels he has to do, and even says “thank you”. Han’s offer of help is twisted into being his blessing to kill him. No doubt internally, his self-loathing for killing his father is going to fuel his anger from now on.
It’s been said before that Kylo is the anti-Luke. Luke rejected the dark by refusing to kill his father. Kylo rejected the light by killing Han. Just as we were seeing Luke’s journey to becoming a Jedi, we’re seeing Kylo as an only partially formed villain.
TFA has many issues, but a lot of your criticisms seem to be a bit of a reach.