My husband left me and he was paying my rent, can my landlord force me to move?

If no one is paying rent why should you have a right to stay there? Your arguments would be with your husband, not the landlord, who is entitled to collect rent for the unit.

You can apply to the court to have your spouse pay the rent, but in the absence of payment the landlord can evict you.

If you are behind on your rent, your landlord can evict you.

Yes. The landlord is entitled to rent. The rights of the landlord are not modified by any complications in your personal life.

Unfortunately yes if the rent is not being paid. There are very specific procedures that must be followed, however. You should try to talk to your landlord before any noticed get served upon you and seek out resources for help to avoid an eviction. Even a filing on your record can cause serious damage to your rental history.

Your rights and liabilities would be governed by the terms of the lease. Some leases allow you to vacate so long as you give written notice (normally 30 but I have seen some for 60 and 90). But some very landlord friendly leases actually have a required initial term (usually 1 year) and you actually CANT vacate early EVEN if you give notice and lots of it. But from your question it actually sounds like you don't want to move, but you simply will now have trouble paying the rent. Unfortunately, unless your landlord is nice and wants to work with you, he/she is not obligated to just give you leniency on the rent even though your sudden financial constraints are not your fault. You didn't mention this, but you should actually start thinking about your rights at separation, such as spousal support and/or splitting of bills/debts, since having those addressed will eventually lead to a resolution of the apartment issue. You should consult with attorney right away to discuss such rights, especially if a separation agreement is not realistic and you are unfortunately looking at having to go to court