Work with your public defender as best you can. Whether or not the charge of DWLS w/ knowledge is correct is another issue your lawyer can investigate. If there is an issue as to the search, your lawyer may be able to file a motion to suppress and if successful the gun would not be allowed to be used as evidence. The reason for the search was likely that they intended to arrest you and felt that a search of the vehicle incident to arrest or what is called an inventory search was called for, but depending on many facts you may have a suppressible issue.
I cannot say what your plea bargain offer will likely be except to say that if this is your first offense it may not include any jail time or even an adjudication of guilt. A lot depends on the judge and your PD will know his or her habits better than most people on here. If any sort of transfer to county court is possible that would be a good turn of events as you would be avoiding a felony record. Even a felony withhold can have consequences later in life in many cases (see my legal guide on adjudication and withholds and what they mean in Florida). Any offer for diversion would be great. Be wary of probation as it is all too easy to violate.
Finally, get a concealed carry permit. Good luck!
According to FL law, you have an affirmative duty to change your address once you move. When you are sent a notice at the address of record, it is presumed you received it; therefore, you had knowledge of the suspension and drove anyway.
A DWLS without knowledge is a traffic infraction; once you are imputed with knowledge, it becomes a traffic crime and punishable by jail. On your third DWLS, with knowledge, you become a Habitual Traffic Offender and you lose your license for 5 years.
They have a lawful search incident to arrest (probably). There are too many unknown facts to ultimately decide whether a Motion to Dismiss should be filed. Your PD can depose the cop, i.e., ask him questions under oath and get his side of the story, which the judge is more likely to believe.
If your arrest was just for a misdemeanor, you were not charged with Possession of a Firearm by a Convicted Felon. Work with your PD. Most likely, you'll get a withhold of adjudication and depending on your judge, maybe some probation. I still don't know why the firearm was a problem, if it was properly stowed. Follow the PD's lead.