Most likely nickel, not chrome. Have never heard of a chrome plated sax in the 1920s, but lots and lots of nickel plated ones.
It's not usual for springs to be plated; in fact it's very bad practice due to hydrogen embrittlement, but if it's lasted that long it's obviously not going to be a problem. Just clean it up with some steel wool, put a bit of oil on it, and it'll be good for another 100 years probably.
You'll need to replace that pivot screw, and it's not going to be easy to find one. Best way is probably to get with a tech with a small lathe and have him turn up a few of them. Note that there are at least two kinds of those pivot screws - you have the kind with straight sides, but the later ones have a taper - and I don't know if they're interchangeable. Another option is to clean the whole post real well, use Loctite (the light duty stuff) to lock it in place, and do all the work from the other end, if it's possible. I've got a couple posts on my bari like that.
Some years ago Ferree's still sold the wee set screws - I STRONGLY advise you to buy a dozen or so. You're likely to find some sheared in half, some stuck in the posts, etc.
As for pads, I would STILL recommend standard tan pads with flat metal boosters. Rivet pads will make an already soft-sounding, low-projecting horn even more so; the boosters will add just a little "sparkle" or "bite" and make it sound a bit more like what we expect saxophones to sound like.