I've had a 2001 TailGator as well for the past 15 years and might be able to answer many of your questions. I fitted mine with a 5kw generator and added a second battery but that might be the only difference.
I just pulled mine out of long term, uncovered, storage and unfortunately it's a wreck and needs a lot of work.
Pay attention to the screws that hold the steel garage door frame to the aluminum trailer frame. They used (in my opinion) the wrong type of screws back there to hold the frame in place. Those screws will work loose and the garage door frame will move and pull the rear trim pieces away from the sideing. If not addressed quickly you'll have all sorts of water damage to the garage floor that will leach up and possibly into the living area. I just finished replacing half the flooring in the garage and much of the flooring in the living area. This is not a job for the faint of heart.
Check the condition of the filler hose from the trailer fuel cap into the tank. It's almost 20 years old and you'll notice it's probably crack to pieces.
Here in Texas, the single AC on this unit is not capable of maintaining much less than about 76 degrees in the living area. We have blocked off the garage supply air units and blocked off the shower sun roof and all other sun roofs to help keep the trailer cool.
If the awning has not been replace check that carefully as it will probably need to be replaced.
If the unit has been sitting, as others have mentioned, replace all the tires. They will blow out. This unit has steel wheel wells so a blowout (I've had so many I lost track) won't damage the flooring but it will typically rip off the plastic wheel trip and usually damage the aluminum and the material underneath.
The graphics on ours started peeling quite a few years ago so we've gone ahead used a razor scraper to remove everything on the side except the top stripe on the sides and the front logo.
Check all the latches on your cabinets and I think you'll find most of those are in poor shape.
Check that the refrigerator will fire off when using only propane. The nozzle will get plugged up and the vent area for the refrigerator rusts out and blocks the venting of the flame exhaust. We vacumed our and cleaned the nozzle and it works fine again.
Right now our two fresh water tanks will not hold water and I suspect they are cracked but I haven't gotten that far. Our black water tank sprung a leat at the drain fitting to the tank and I had to replace the whole tank a few years ago. It wasn't a hard replacement but replacing a tank isn't on my top 10 fun things to do.
About 7 years ago I had a reason to pull the exterior cover under the bedroom around the trailer hitch. I found the tongue had a crack and needed to be welded.
The rear leveling jack will easily drag and bend on even small gas station entrances that are not level. After replacing the rear leveling jack twice I just left them off.
Here is what the damage looks like under the vinyl in the garage and living area.
One last thing, check closely for delamination of the fiberglass siding near the rear of the camper on both side.
https://photos.app.goo.gl/ihkaJSMHeJxdSiYx8