It's Cersei, not Joffrey who orders Robert's bastards rounded up and murdered…just one of the several ways HBO softened her up from the books.

Ser Friendzone!

I think you might be forgetting the strong possibility that Mad King is Tyrion's real father, making him half Targ…which means the Dwarfism could have come from him.

R probably married L, he was allowed to as Crown Prince. Better than marrying all his sisters like one of his ancestors. :-p

She's old school loyal because her father told her to come serve him.