In Alberta what is the age you can move out of your mother's house and into your mother's ex-boyfriend's house?

It would never make any sense to do this at any age. Even if the boyfriend was never in a parental role, this man was with your mother, and to some, this makes him out of bounds. Recommend that if you decide to do what is not sensible in this case, that you wait until you are in your 20's and have some life experience. If you are under 18, doing this may create some legal difficulties for him.