I took my gas tank out and noticed that there is some rust at weld locations and seams. Is the car rusting from the inside out? Or do you think this is surface rust that I can grind down and paint? Pictures below

 

POR15

 

spot welds are vulnerable , that is very light surface rust, nothing too serious. I would rustproof those areas or paint them as noted above. Definitely treat them to keep them from rusting further.

 

Its just surface rust. Welds are prone to that.

You can wire brush that off and POR15 it or something similar.

Look into "honey seal" or woolwax's "creep n crawl". Its a hardening wax that's similar to what is used at the factory inside of crevices. You can lay it all over the seams and welds under the car.