I signed a one year that ended over a year ago. I have continued to pay my rent monthly. I gave landlord 30 days notice and moved out. Two months security was taken when I first moved in. I wanted to use part of security as the final month's payment.
I live in New York. I have two questions: 1. the lease states "Security deposit shall not be used as last month's rent" Can I and do I have a legal right to use the security deposit as final month's rent? 2. The lease also states "Tenant must provide 60 days notice prior to lease end date to vacate apartment". Considering I was paying month to month, I am under the impression I only had to give 30 days notice. Please help

No, you were still under the terms of the rental agreement, so you still have to give the 60 days notice.
So you will owe them 60 days not the 30.

Next no you have to pay the last month month rent ( well the 60 days rent) and then you will get the security deposit back minus any damages to property of course.

If the landlord will agree to use it for last month but then he risks damage to property if you leave it in bad shape.

Also the landlord can agree to accept a 30 day notice, but does not have to, they can hold you to the 60 days.

Your mistake, the terms of the lease merely change to a month to month agreement, but the terms are still valid unless you signed a new agreement for a month to month

Thanks. But I have been told I am only responsible for 30 days. How would I go about looking up the info for my state? Is there someone I could call in my state? Thanks again

It would be if there was not a lease agreement that you are obligated to, a verbal month to month is 30 days.

The issue is that a lease does not just "end" if you continue to live there. All of the terms of that lease live on except for the amount of money you pay ( that is changeable with 30 day notice) and the fact you can leave anytime ( not obligated to a year) with the notice listed in the lease.

You are still under the lease, that is the issue, so what state law allows for verbal rentals, does not matter ( it would be 30 days) what matters is the term listed in the lease.

What if I I left a message on the answering machine about the 30 days notice and then the landlord returned my call and said to put it in writing. I put it in writing and gave it to the landlord. Would that be considered agreeing to it or do I need the landlord to sign it?

If you gave 30 days and the landlord accepted then you are OK. But you would have to prove he accepted it.

What's the issue here? You said you already moved out so is the landlord billing you for 60 days rent or what?

what if I I left a message on the answering machine about the 30 days notice and then the landlord returned my call and said to put it in writing. I put it in writing and gave it to the landlord. would that be considered agreeing to it or do I need the landlord to sign it?

Landlord agreeing to change the notice provision from the 60 days specified in the lease to 30 days? No, I see no agreement in these facts.