I am buying a home in Oklahoma, I have a rental lease in a local apartment complex. My lease is not up until February. My question is can I break my lease when I purchase my home without paying any penalties or fines, and the rest of my lease?

Excuse me, but do you NOT understand that a lease is a contract? You should not have entered into this contract if you planned on buying a house.
No you CANNOT break your lease just because YOU chose to buy.

You have 4 options:

1) approach the landlord and ask if they will let you out of the lease
2) approach the landlord and ask if they will allow you to buyout the remaining term
3) sublet the apt if the lease allows
4) find a new tenant to take your place

If you give notice and vacate, the landlord needs to put in a good faith effort to rent the unit. But you WILL be responsible for the rental until then.

Not unless your lease says you can. If the lease has no mention that if you buy a home you can get out of it, you are simply breaking your lease and need to pay all penalties from breaking that contract.