"You're not the first one who's had trouble with money," said Mr. Roberts, scrutinizing Mr. Weasley closely. "I had two try and pay me with great gold coins the size of hubcaps ten minutes ago."

Page 77 in my copy of GoF. So, yes, Muggles can see Wizard money, at least in canon.

It seems to be a convention of fiction. Lots of fictional terms are capitalized when real-world analogues are near-universally left lowercase. (Species names immediately come to mind.)