I think the answer depends on what "pretty mushed" means. And before you read on, here's a caveat: my sole experience with chain link fences is taking them down, not putting them up (but I've taken down quite a few :-)).
That said, my experience is that the links will collapse in on one another, not actually bend. Which means that the fencing as a whole can be straightened out again. Also, even though the posts appear untouched, you should ensure that they're plumb.
The rails are easy to replace; every home center should carry them, as well as the caps and other accessories. The important piece that you'll need is a coupling: a short section of pipe that fits snugly over the ends of two existing pieces, to join them together (in the fences that I've disassembled, this is just press fit, not welded or brazed, but I suspect a dab of epoxy would help).
Cut the existing rails with a reciprocating saw, close to the existing rails that still have caps (you could also use a hacksaw; you won't be able to get enough clearance to use a pipe cutter). Slide the new section(s) of rail through the caps, attach them to the posts, cut to length, and slide the coupling in place.
That just leaves re-attaching the fencing. I think that you can stretch it to the rail using baling wire and a pair of pliers: loop the wire through fence and rail, and twist it to take up all slack. Then attach normally.
I'm not sure what the rod might have been, the inside of an air tank is pretty simple.
Replacement drain valves are available in a variety of configurations, and generally they thread into a nut welded into the tank. It's then just a matter of finding an appropriate replacement valve (relatively easy) and removing the old one (probably much harder).
To help get the frozen valve out, you could (should) try penetrating oil to free what are almost certainly frozen threads, but you may need to step up to using a torch to apply heat to help break the part loose.
Best Answer
There's more than one way to join galvanized wire, and a few ways you can do this. Some are better than others:
Now as for how to do it, you have 2 options: