SOL begins to run on the date the crime occurs. The prosecutor has until the expiration of SOL to CHARGE you. If you are charged within the time limit, SOL requirements are satisfied.
Once charged, speedy trial rights dictate how long the court can take to bring you to trial, (90 days if out of custody, 60 if in custody) BUT that time clock stops when a defendant has failed to appear and does not start running again until he/she next appears in court. So in other words, you cannot escape a criminal charge by waiting it out.
The previous answer is correct. I would recommend that you immediately contact an experienced criminal defense attorney to discuss your preparations for dealing with these accusations. Furthermore, it is important that you consult an attorney who is famiiar with the court where you are charged.
There are two laws that dictate the pre-trial timing in a criminal case; Statute of Limitations and Time for Trial (also known as "Speedy Trial).
The Statue of Limitations controls how much time after an incident that charges can be filed. Some crimes, such as murder, generally have no statute of limitations. Most misdemeanors have a two year limit. SOL is very simple in misdemeanor cases, either it's within the window or it's not.
In addition, the person being charged does not necessarily have to be arraigned, but the prosecution must show they took reasonable steps to notify the defendant. Notice is occasionally an issue.
Time for Trial rights start when a person is formally charged with a crime. A defendant (and presumably the prosecution as well) is entitled to a trial within 60 days of arrangement if in custody and 90 days if not. Although called "Speedy Trial" rights, there are many exceptions to the law that these time frames usually mean little.
In any case, a bench warrant issued before SOL or Speedy trial rules out, tolls the respective time period. What this means is that if a warrant was validly issued the charges remain at least as long as the warrant (and longer in some cases). Warrants can be renewed forever. If the plan is to wait it out until the charges disappear it is not a good plan. You will be arrested someday. In the meantime you will not be able to get a license; may have trouble getting work, housing or government services; and will be looking over your shoulder everywhere you go. It always works that you are arrested at the most inconvenient time (and anything they find during the search subsequent to arrest will probably be admissible as evidence against you in any new crimes). Get an attorney and go deal with this so you can get on with your life.
Statute of limitations means nothing to you because you said, "I have ... old misdemeanor and gross misdemeanor charges..." S.O.L. deals with them time for the state to charge you with a crime assoicated with the evidence that they received from law enforcement.
Now you are dealing with warrants. The warrant STAYS (stops) the running of the speedy trial rule until you are subject tot he jurisdiction/court. You have to appear and be subject to the Judge either in regular court or held in jail so that the court knows you are there and going to be there. Then the speedy trial rule starts and the State has 60 days to have your trial if you are in jail or 90 days if you are out of jail to have your trial. Nothing goes away so deal with it. If you need an attorney you can ask for one to be appointed by the court or hire your own private attorney.