Scrape a spot on the coil, with a knife, and see what it looks like under the tarnish, it may be stainless.
Yes, some stainless will corrode a little, and then it is a protective layer on the surface.
Are ya' pretty sure the lining is zinc?..........Is it a little harder than say, lead?
Scrape it with a knife as well, and make a determination........Lead will shave off very easily.
The coil should clean up easily with a good soaking in some OxyClean or PBW, the nuts on the end of the coil look to have a moveable "ferrule" of sorts that surrounds the flare on the tubing within.
Put a few drops of some good strong vinegar on the box lining and watch for any reactions............It may be galvanized steel, ( zinc coating), although I can't see any rust that would have developed over the years from the cut edges of the metal.
Vinegar, if left to sit, will remove the galvanizing, but if it's zinc sheet, a little scrubbing with a ScotchBrite hand pad and it should clean up nice.
On the coil, let us know what ya' figure out.......If it's copper, I don't think you would want to use it for beer dispensing, ( acidity and whatnot).