2. Arresting Tyrion isn’t a breach of the King’s Peace. Catelyn was very careful to follow the legal forms and would have had dozens of witnesses that she had arrested him for a crime committed in Winterfell and was bringing him there to await trial, as is Eddard Stark’s right as a Lord possessing the right of pits and gallows.
3. She probably wouldn’t face a penalty, given the ambiguity of royal justice and the right of pit and gallows. Especially without evidence of much in the way of royal courts, there’s not much of a sense that there is a right to be tried in a royal court as opposed to by a lord.