I'm new to cellphones and can't seem to find an answer to this: I know I can receive calls and voicemail if the phone is on standby, but if I "power off" the phone will I still be able to receive voicemail? I do have a voicemail plan, just in case.

Yes.

Are you certain, only since posting here I asked a friend who owns a blackberry and he said if the phone is powered off and someone calls, they will get a message saying the person (or number) is unavailable at the moment?
Thanks in advance.

Yes, I'm certain.