I would like to date someone, however he has a drug convition (felony), and before we take it to a new level, I need to know if my career path will prevent me from ever living with him. So, Can a convicted felon live with a teacher.

This is up your contract with the school. There may be a morals clause that might prevent you from doing this. It might depend on the nature of the felony.

Can you, normally yes, but it may have effects on promotions, it may in some schools, or school systems violate some of the rules of employment.