Hi, Mike, welcome to the forum and the wonderful world of Airstreaming.
We have the 2006 23' LS model and have been happy with it. It has a mark on the right side where the original owner had a limb fall on it. He kept the insurance check and sold it to the guy I bought it from. There are no leaks, all cosmetic, all rivets intact. We were happy to get it and intend on keeping it and enjoying it for the rest of our lives. Our children can decide what to do with it.
Your power jack won't work if you have no batteries connected. The jack is directly wired to the batteries so even if you have the TV connected there is no power. If you can afford them, Lifeline AGMs are one of the best, but they are expensive. You can also just use marine/RV deep cycle batteries which are lower cost. I recommend Deka brand but they are hard to find. Lowes carries them but has only a 90 day warranty.
I replaced our batteries, which were older but still working. I thought they were pretty weak but it turned out the converter was bad, not charging them. I replaced it with a Progressive Dynamics 4655 and all's well.
I have the old Lifelines in the garage, they hold a charge of about 85% for a long time.
We had ours resealed and rain stress / pressure tested at Airstream in Jackson Center, OH in 2015. At that time labor was $120/hour. Strip and reseal the entire top was $1,000. We do not have any leaks but the roof hadn't been resealed for more than 5 years and we were concerned. I had them fix a soft spot in the floor (I removed all the furniture in the front to save on labor) and also clean the existing front floor to remove most of the mold stains.
The PO gave us his Equalizer hitch along with some extra tools and parts, a small cost savings for us. He had just replaced the awning too, so another bonus.
I think the answer to many of your questions is to repair/replace stuff when necessary and when you can afford it. Leaks take priority, in my opinion. Enjoy the AS and don't worry about resale so much. If you're a DIY kind of person then do as much as you can yourself, especially anything that will save on labor costs. Google what it is you're looking for, like "Airstream corner mattress", then check the dimensions against yours. Airstream will sell you what you want but there are other sources.