For the PVC... PURE acetone, of course, is the first remedy. Don't breathe in, don't use near fire!!
In terms of the spots of black encrustation... not as simple an answer. However, be careful. The surfaces here have already been treated with SOMETHING; whatever solvent/acid you try to use (Jeweluster, MS-70, Nic-a-lene... Google these if you're not familiar with them - and if you indeed you AREN'T familiar with them... probably best not to try on these!) may not react well with the surface because of that. You COULD end up with something splotchy-looking.
IMO, the surfaces of both those coins are already etched beyond saving. As long as no abrasion is used, none of the chemicals I mentioned above will harm the 8 Reales. I'd leave the other alone or send it to a profession to see if they want to try something.