Just one point, but Kylo worshipped him as Vader, not Anakin.

And we get to know more about his relationship with Han in all three movies; he finds out from Snoke about Han and says, “He means nothing to me,” he senses Han on Starkiller Base and also implies to Rey that Han was a disappointing father, after killing him he is traumatized, something Luke and Rey point out, respectively (“Strike me down in anger, and I’ll always be with you. Just like your father;” I also just rewatched TRoS for the first time today, Rey points out to Kylo Ren that he’s haunted by his killing of Han).