First, welcome to NAVSCOLEOD.
Firearm registration - go to the Security Forces building, located right next to the library. If you're coming from Niceville/Valparaiso (the east gate), keep driving down Eglin Pkwy towards the other side of the base, pass the Air Force Research Lab on the right, go up the little hill, and not too long after you get to the top, you'll see a road to the right just before the library (if you've hit the flight line or the climate research hangar, you've gone too far). Take that right and the Security Forces station is just up the road about 200 meters or so.
TMO - If you're coming from Niceville/Valparaiso (the east gate), keep driving down Eglin Pkwy towards the other side of the base, you'll see Eglin Federal Credit Union on the left hand side, take a left at that intersection, follow the road (it curves around, just stick with it) until you see a nondescript white building on the left hand side, with a parking lot in front of it; that's TMO (they close at 1500 by the way).
Weigh Station - If you're leaving base through the east gate (towards Niceville/Valparaiso), keep driving down Eglin Pkway towards the range; the weigh station is about 4 miles down the road on the right hand side, across the street from Goodwill and a small strip mall. You'll see a gravel parking lot, with a gray one-story building, and several mounds of rocks; turn right into the gravel parking lot and walk inside the gray building. I think they close at 1630, and the price for weigh tickets is $4.
Good luck in school dude.