I'm moving out of my apartment Dec 1st and I want to know, if I paid my last months rent when I paid my security deposit, does it mean I don't have to pay rent for the last month that I'm living here. I gave my 30 day notice, and it was my choice to move out. Please advise.

If you have already given the landlord payment for the last month, November, then you have paid until November 30. Check your rental/lease agreement for exceptions.

I was going to pay November's rent today. I just wanted to know should I pay? Even though I paid it in my deposit?

It depends on what you paid. If you paid 1st, last AND deposit, then no, you don't have to pay November's. But if you just paid security then no. While the landlord can choose to apply security towards unpaid rental, the tenant can't decide to do it.