so, do you want to leave or stay?
as you suggested, if you don't have a specific term lease, give notice and leave. You seem to be demanding things be done that are not issues of habitability and since there is no lease, I guess they there are really not enforceable promises, right?
btw: rent is due on the first. The grace period is simply that; a grace period where the LL does not charge you a late fee. It does not mean rent is due sometime between the first and the seventh. He can actually give you a 3 day pay or quit notice on the second of the month.
If you do not believe the LL has given reasonable notice to enter for the repairs, then don't let the repairmen in.

