You are not required to answer the door when the police ring the bell. That being said, if the police have a warrant, or are responding to an emergency, they can force entry. If you do answer the door, you do not have to let them in unless they have a warrant.
It is possible that the probation hold is keeping him in jail, but the DUI is the lead case. If he saw the judge on the DUI, and has an attorney for that matter, you should consult with him or her regarding the probation hold. Typically a probation violation will tail a new offense, and will not be sentenced until the new offense has been resolved.
California Penal Code section 1203.4 allows you to petition to have a California conviction dismissed once you have successfully completed probation. As the answer above suggests, a lawyer who is licensed to practice in California could help you prepare and file that motion. The fact that the case happened over 20 years ago should only help your cause in getting the conviction expunged.
The court will look at your income, your expenses, any debts that you have, and any assets that you own (like a car). Based on the information that you have provided, you should qualify for the public defender.
A no contest conviction is still a conviction in Utah, and should be reported. The laws of the State of Utah allow your conviction to be expunged, making it as if it never happened. If you expunge the conviction, under Utah law, you can act as if it never happened.
Depending on your record, and how strong the prosecution feels their case is, you could get the reduction to a misdemeanor. You may also qualify for drug court, which could result in your case getting dismissed. Based on what you've said, the officer did not have your consent to search vehicle. You should consult with an attorney to see if the evidence in your case should be suppressed.
I agree that you need to consult with a civil attorney regarding this matter. If the defendant owes you money, and it appears that he is trying to hide money through liquidation, your possible remedies are at stake. A civil attorney can assist you in protecting your rights and options in the civil case.
The answer above is correct, generally an arrest and dismissal will show up on your record. In your case, however, no fingerprints were taken. Without fingerprints, some agencies will not record an arrest or disposition of a case. It sounds like this is the case here. That being said, the local court and law enforcement will still have their record, even if BCI does not. If you want everything cleaned up, you can petition for an expungement. If you are happy with the current state of your...