Another interesting aspect regarding Kylo that is apparently in the novelization, is that killing Han didn't accomplish what he wanted it to for himself. He was wrecked with guilt and trying to suppress the light during that fight with Rey and Finn.
From Reddit:
I got some of that from the film tho leaving it open is even cooler (ie. movie novelizations are a fucking plague).
what I like about it is Snoke reacting in the "we must finish his training" way cause whatever they throw at him in terms of making him bad will end up distorting his whole thing even more and make him more dangerous / less predictable. He's just a fucking wild card (lightsaber being all fucked clearly reflecting that).