Very simply get a good criminal defense attorney. If you are just a suspect your attorney may be able to keep you out of the soup. If you are already charged, your attorney may be able to keep it from having harsh consequences rain down on you. You can find just the attorney you are looking for on this site.
In general, you can't be convicted without "a" trial, but you can be convicted without you being "at" the trial. If you were convicted in your absence, and the court had an error (like sending you an incorrect court date), you can have an attorney address this for you and potentially have the conviction set aside and a new court date issued.
Even though any attorney licensed in the state can represent a criminal defendant without practical experience in that area, they may still come up against ethical restrictions that may require that they seek assistance from more practiced attorneys, or other restrictions or considerations. This is especially true when representing a client with felony charges. The attorney you choose for representation should be aware of this, and you need to understand the implications as well.
Full disclosure is the best decision, regardless of whether you could lie on the application and get away with it. They need honest teachers, not dishonest ones. Even though you answer yes to the question, you will get an opportunity to explain the circumstances surrounding the original charge and how you have learned from your mistake, matured since your youthful indiscretion, or whatever was the issue. Just be open and honest and expect the best.
The pawn shop is disputing ownership because they likely don't want the police looking at them with a scowl for having stolen property. After all, they gave someone money for the property that you are now saying is yours. That doesn't mean that they get to keep your property, if you can prove it's yours, though. It sounds like you have more than enough to overcome your burden of proof that the items are yours. Do you need an attorney? Maybe not. But if the value of the property being returned...
Technically, no, but I would strongly caution against it. The reason we subject ourselves to the grueling years of study (which never ends) and testing to become criminal defense attorneys is because we want to help people that are in situations such as yours. This difference is why you can expect better results with an attorney on your side than attempting it on your own.
This is a public forum that is just as accessible to law enforcement as it is to you. When you post a question try to be as general as you can. You can be detailed with your attorney that you can find on AVVO.
While you are contacting the police with the expectation that they should do something, there really is nothing that can be done absent something from the court. Getting a family law attorney that can file a Motion for Enforcement should give you what you are looking for.