This is because you have a OEM version
Also, the firmware appears to be G7Z9. Should I upgrade the firmware and to what version?
Burn a DVD first and see how things worked out, upgrading firmware can always be done.
Also, are there any tests I should be running on the drive to make sure it is being recognized correctly and/or is set-up correctly? What software should I use?
Your drive is recogniced correctly because it's a OEM version. I use Nero, but you can also use any other burning software. First burn a disk and use Nero speed tool to do a quality scan. Only then you can see if your drive works as it suposed to do. We can't give you advise until we see a quality scan.
P.S. If I upgrade the firmware and the drive turns out to be bad, do I void the warranty?
If you stick with OEM firmware (start with Letter G) you won't void warranty.