Thanks! I disagree, though, I believe
Spoiler
he diverted from the path to exit the castle grounds, I believe he could have just as easily made for the free cities with his father alive. Killing his father was revenge, not a tactical move.
Yes, i think so too.
Spoiler
He asked for a hidden way to the chamber of his father to kill him. Tyrion also mentioned that when he was talking to Jamie.