Painted Bakelite is an easy fix, because it's impervious to paint stripper (unlike modern plastics). All the old 1930's Bakelite fitting in my place had been painted over, but a quick brush over with Nitromors cured it.
I would do a test-area first just to make sure it is Bakelite, though...

Can't help with the ID, but I think that the shade (probably 1970s-80s or later) is newer than the fittings (1940s-50s). But these are just guesses.