OK we drove past the RV CG in Lajitas and looked in, it had trees which is quite unusual for the are and was obviously a cut above the dirt parking lot cg's that make up the rest of the selection. There are a couple CG in the Sturdy Butte/Terlingua area. Plus there is a FHU cg in the park itself. There are lots of places around the park with no services at all.
Don't worry about gas, there is are several service stations in the area including at least one in the park. The gas will be somewhat pricey but it wasn't outrageous when we were last there. There is a small super market in Sturdy Butte too.
Firearms? This is Texas and the parks follow local law.
A lot of businesses shut down for summer, I'm not sure when they re-open. I highly recommend the River Road as one day trip.