Before he was the emperor, he was a successful high ranking Senator from Naboo. It's not far fetched at all to believe in that facade of a life, he had a child. Maybe even a wife at one point. He's a master manipulator, he hide his identity for decades, not a stretch to imagine a cover that involved a kid.
It all just happened so fast.
Pacing and lack of emotional weight is my issue, not so much the plot it self.
That said, he had his son murdered then?
They sped over that part too. And was his sun Tom hardy? Looked like him.
Re: Rey claiming a Skywalker, it worked for me because it was her choice. No one gave her that, no one forced on her what they thought and who they thought she was. Letting her make that choice for herself was powerful and I'm totally cool with her, she's allowed to identity however she wants after all she's been through.