[Were there any bastards of Tywin Lannister?]
He'd have you flogged for the mere suggestion.
[Where was Oberyn Martell during the rebellion?]
Good question. Offhand, I don't recall the answer. Maybe in Dorne, maybe across the narrow sea with a sellsword company. I'd have to check my notes to be certain.
[Was Gregor Clegane knighted at Harrenhal?]
Don't think so, but again, I'd need to check my notes. I think Gregor was already a knight.
[Have there ever been a ruling Lady of Winterfell or Queen of Winter?]
No. Although I do hope to someday write the Dunk & Egg story where they travel to Winterfell and meet the She-Wolves.
[Are highborn ladies trained to a lot of practical things, like serving guests, making cheese, and so on?]H
Sansa is more than just a young lady. She's the daughter, not just of a noble, but of one of the most powerful nobles in Westeros. The great houses stand far above the lesser nobles, as the lesser nobles do above the smallfolk.
She would not make cheese, no. But Arya might think it would be fun.