The drive-train issues may well just be caused by the chain being tight - I'd try splitting it and soaking it in oil myself as replacing it on its own is unlikely to be practical (you will more than likely need new chainrings, a new freewheel (won't be a cassette at that age) and maybe rear mech.
If the freewheel is sticking (not free-wheeling or slipping) lubricating that might help.
Cable inners and outers are fairly universal as far as I'm aware so, assuming you can get white, replacing those should be trivial.
Bar tape should be obtainable from a LBS but if you want to stay period you might struggle.
As for the (what look like) rust spots on the chrome bits - brillo pads and elbow grease followed by a light coating of wax should sort that out
Can't wait to see the finished article!
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Just a y2k FSR with some modern bits