Soldiers and Sailor Relief Act exempts militay from taxes in the PCS state for the most part. So unless you moonlight you don't have to pay income tax. If the spouse works he/she will have to pay taxes on that.
Sales tax if paid in another state on your car is exempted from the PCS state.
Check with your legal office on the base.
I can't speak to the gun license issue. A lot is done without specification in the law in NY. I do know military who have put their pistols in the Armory on base until they get a state permit. Usually to get it out of the armory you have to display your permit.
I'm not a lawyer nor do I play one in the movies. Do your own research
Cogito, ergo armatum sum