Nope, you're not really missing anything. The shock link has failed and will need to be replaced; but getting them apart can be a challenge. The "head" of that "bolt" is just a washer that is welded to the pin, sounds like your weld has broken and the pin is turning inside the washer (as well as inside the shock arm).
The easiest way forward may be to cut the link in half, so you can remove the shock and cut off the nut.
For the bolts to the frame, I've got an old Craftsman thin-wall socket that will fit with some persuasion (tapping with a BFH), but the new ones are thicker and won't fit. I would suggest trying to grind down a socket until you can drive it in there; but if it breaks rather than turning the bolt, you may have to drill the bolt.
Then convert to socket-head cap screws (which are stronger anyway) and buy a hex bit socket to suit.
Oh, and next time, just fill the shock through the plug on the side
