Is my landlord allowed to demand rent without a contract?
Sure. In most jurisdictions, not having a lease means the tenant is term-to-term, usually month to month. The landlord is allowed to ask for more rent prospectively. Some jurisdictions have a minimum advance notice requirement, but it's unlikely to be longer than a month anywhere. That means if you pay your rent on January 1st, the landlord can say he's raising the rent effective February 1st, unless your jurisdiction requires a longer notice period. But almost anywhere, I'd bet he could say he's raising the rent effective March 1st.