Especially for AU, aging up is totally fine and even encouraged in cases where the character being a bit too young might not be appropriate for some of the mature themes in the game.

And yes, being part of one faction but living in another area would be fine. For pure IC reasons, if the character wanted to buy a house they'd probably be socially expected to purchase and maintain it in their main faction's city and commute or otherwise stay in the dorms while in the other faction's city.