Congratulations. I don't see why you couldn't. Prisoners under a death sentence in California can get married, so your warrant would stop the process.
Do you think you might get arrested at the clerk's office? I think it is highly unlikely. I'd stay away from the DMV, though. You will also not be able to get a passport or leave the country, so if you're planning to honeymoon in Cabo San Lucas, cancel those reservations.
Should not pose a problem. Why not stop by the court where the warrant was issued and put the case on calendar? Better chance of staying out of custody
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.