Yes, it's possible. In fact it's no less important to perform backups the same as if mirroring weren't enabled since the database is in the FULL recovery model. No changes have to be made to perform the backups.

Mirroring doesn't change the LSN's either. It only looks at them to make sure the principal and mirror are in synch.

I haven't tried this but I understand you can even mix a log shipping configuration with mirroring if you wanted a standby server in addition to the mirror/principal.

Have a look at this article for more detail:http://www.microsoft.com/technet/prodtechnol/sql/2005/dbmirror.mspx