You can move next week, but you will have to continue to pay rent. You need to give notice written notice prior to the the first of December unless you want to owe January's rent as well. A 30-day notice is also required for the landlord to make you move... the protection works both ways. Yes, it's legal for the landlord to ban your boyfriend - any landlord can decide who is on his/her private property for valid reasons... although typically, it's only if your boyfriend (or any guest) were to stay over for too many nights -- 14 nights per year in most cases. You can get rid of the mold with bleach -- it's pretty simple, and you need to put in a written request for repairs for the issue of the kitchen smelling like a bowel movement (there may be sewer issues going on). You will have to pay the full month of rent for December, but you can choose to leave tomorrow if you want to. Give notice prior to December 1st unless you want to be held responsible for another month of rent and make sure that you notify the landlord verbally and turn in a written notice as well. Make sure that you do a walk through with the landlord prior to leaving the apartment, and if you haven't turned in work orders for the necessary repairs or issues, especially the mold on the walls, you could be held responsible for not reporting the issue to be fixed. Make sure that you clean well before you leave and have the landlord sign off that the place is cleaned -- otherwise they'll hire a cleaning service that can easily cost you hundreds. Good luck to you.