Can’t comment on the wiring issue, we had things done by a competent person, because we aren’t, but I know Marcolm did his himself so he will be able to advise.
On the polishing it depends if it’s solid brass or plated, and whether it has been lacquered or not. Test it with a magnet and if it reacts then it’s plated and polishing might end up exposing the base metal if it’s only thin plating. If it doesn’t react and is solid brass but has been lacquered then to polish it you need to strip the lacquer with something like acetone before you can polish it.
If it's just the cable you can see running up the chain you might find the connector if you unscrew the top part of the light. Even if there is no connector there will probably be room to join a new cable with some wago connectors.
If unlucky the connector will be a crimp connection that connects all the lights accessible by unscrewing the bottom of the light. You'll need lamp wire - a gold fabric covered wire.
For the finish some were made to look old and probably won't polish up shiny.
I doubt if it has any great age. A really old fitting would have been built with gas, oil or candles in mind and will have been converted as in the case of many brass wall lights and table lamps. That dusky bronze/brass look is very repro too, as I'm sure anything properly old would have been polished, and that shows no signs of the light green deposits that come from being polished.