Yes, in books about post-Alexander Hellenic civilizations it mentions that the vulgar nouveau-riche Romans were quite taken by Grecian sculptures and paintings.

If they couldn't buy it then they resorted to "liberating" these works of arts.

And not unexpectedly, there arose a whole industry in Greece at creating knock-offs and counterfeits. They even got quite skilled at "ageing" these same works of art.

Yes, there is in fact a style that developed during the Hellenistic now called "Archaizing" which, naturally, is when sculptures adopt the aspects of Archaic art. This is a good example from Herculaneum.

Not too much I can think to add, but usually you can identify these by the comparatively naturalistic clothing over stiff, highly formalized poses.

Great question. Following that, if someone can answer why we (contemporary western ) choose to collect and distress /damage new items to emulate an old aesthetic.