So only two lines - one suction and one return. If you do find a main drain, then it is likely tied into the skimmer. The picture of the skimmer with the blue "GIZZMO" in it shows the second opening plugged closed. Either there's no MD or there may be one but, because it was leaking, they simply sealed it off....definitely lots of intrigue with a buried pool.
As far as the coping and concrete goes, I suppose it depends on how much you want to spend? If you want to truly renovate this pool and make it "your own" then redoing the deck around the pool and adding on new coping (perhaps with a more modern liner track) is the way to go. If the desire is to just get the pool back to life and not sink too much money into it, then leave everything as-is as much as possible including the plumbing. Buried PVC pipe should have a long expected life (about 40+ years) assuming it never suffered any freeze damage. The returns in your picture look like they were plugged and so there's hopefully no water infiltration. If the pipes at the pad are looking damaged, then all you might need to do is dig down a foot or two, cut the old pipe away and stub up new connections. In order to completely redo the plumbing, some portion of the deck would have to be cut away to access the return pipes and install new ones. Digging under an existing deck is dangerous and you'll never be able to backfill it properly which could result in the deck sagging and cracking.
There are actually 2 returns

If you look there is one on the left with wire coming through it and one straight ahead.