“Also puts a different spin on Tywin always saying to Tyrion that he was not HIS son. Maybe the problem between Tyrion and his father was not about his being a dwarf at all; but, Tywin was actually speaking the truth -— he is not his son.”
Yes, and some of Tywin’s dialogue really does point to that as something Tywin suspected. For example, he says at one point something like “I have to suffer you prancing around with the sigil of House Lannister because I can’t PROVE YOU’RE NOT MY SON”.
Now that harks back to the laws of legitimacy, which say that any children born to a married woman are assumed to be trueborn sons of the father, because there is no way to prove they are not his son. He’s practically saying that he knows Tyrion is a bastard but he can’t legally prove anything so he was forced to treat him as a son.
Tyrion thought the whole attitude was just because he was a dwarf, but Tywin always denied he cared about that when it came up, his grievance was always that he didn’t think Tyrion was his son.
And Tyrion's last words before Tywin killed him, "You're no son of mine".
I think Tywin will ride that green dragon in battle. If Tywin and Jon Snow both have Targaryen blood, they may both be dragon riders.