Last month's rent applies to the last month you will be staying at your unit. If you give 30-days' notice of your intent to vacate then you may keep your money you would otherwise pay your landlord and use that last month's rent, which cannot be used as your security deposit to be offset for damages (the security deposit is for that purpose).
The first and last rule generally means that when you move-in you are required to pay your first month rent and your last month's rent. A security deposit may also be charged. But oftentimes your landlord will work with you in making security or last month's rent deposits. The difference between last month rent and a security deposit, both which can equal the same amount, is that the last month rent is used to apply to your last month of rent, while the security deposit is refunded to you provided you leave the apartment in good condition minus reasonable wear and tear. Your security deposit is generally not applied towards your last month's rent, especially if you did pay a last month's rent in advance.
You can't apply a last month's rent deposit unless this is your last month (or, in your case, the last two months). I don't know what state you are in, but it is unusual to give a two month deposit. If you have a rental agreement that requires 60 days notice to terminate, I guess that would make sense. But, unless you've given notice, then, yes, a prudent landlord would give a late notice.
Yes. If you mean 'the rent for last month', certainly. If you mean the 'last month rent deposit', probably, if the rental agreement states that the deposit was to have been funded.
No. Your last month's rent is that: your last month's rent. The landlord must allow you to stay in your apartment for the last month and not use that money for any other reason. If the landlord collected a security deposit then he can use it to repair his unit: IF you are the one who damaged it outside the realm of normal wear and tear. He cannot use your security deposit as your last month's rent unless you agree to it.
== == Usually paying the last month rent means you pay the regular rent plus a closing fee which means if there are any damages done to the place that was not there before you then you have to pay so much for that too. == == The usual practice is to pay the "first and last" month's rent when you move IN to the unit. This means that the owner is holding a amount that is equal to the last month's rent that you occupy the unit. This is so you can't skip owing rent.
No, unless you're moving out.
yes
Yes you can. Your landlord cannot use your last month's rent as security deposit and vice versa.
at that last day
If there was a lease, the landlord has an obligation to try to rent it. Until then, the tenant owes the rent. If this was a month-to-month tenancy, the landlord should keep the first month's rent, and return the security deposit and last-month's rent, if any.
Yes he can. Deposit usually cannot be higher than a month's rent. Last month's rent may not be used as a deposit.
Yes.