Can I re-install OS X on an encrypted drive without the password? I don't know my password to my Mac OS X account and it has file encrypt enabled on drive. If I reinstall Mac OS X, will it require a password to do so?
No, you do not need your FileVault password to erase and re-install OS X.

Without your password you will not be able to recover the existing files, but you will be able to completely blank and reinstall OS X on the Mac.