anyone had any success cutting/shaping and finishing off (to a
reasonable standard) marble surfaces?

I have acquired a piece of marble ~15mm thick to finish off the "tap
end" of the bath where previously a lot of daft awkward-cut tiles were
bunged in with silicone etc etc and leaked.....

The bit I have is salvage and has some minor surface scratches and a
few stains - assuming I can cut it with (of course) the angle grinder
+diamond blade / elec tile saw :-

what are my best options for dealing with surface stains and
scratches? can you sand it with fine wet and dry?

then how best to polish/seal? for use in the bathroom??

thanks in advance

JimK