Actually, month to month isn’t a lease at all! When you are month to month, you don’t have any contract at all!
Month to month is a contract and if a landlord does not have his own, then it reverts to the state models .
Yes you do.
The state laws usually treat it as an implied contract. So even though you never signed an actual lease, as soon as you move-in, by law, you are bound to a contract, since the law has determined there is this minimal contractual relationship that exists in any landlord-tenant situation.