rodent native to South America, 1660s. It does not come from Guinea and has nothing to do with the pig. Perhaps so called either because it was brought back to Britain aboard Guinea-men, ships that plied the triangle trade between England, Guinea, and South America [Barnhart, Klein], or from its resemblance to the young of the Guinea-hog "river pig" [OED], or from confusion of Guinea with the South American region of Guyana (but OED is against this). Pig probably for its grunting noises. In the extended sense of "one subjected to an experiment" it is first recorded 1920, because they were commonly used in medical experiments (by 1865).
to win something hands down (1855) is from horse racing, from a jockey's gesture of letting the reins go loose in an easy victory.
The Two Thousand Guinea Stakes was not the best contested one that it has been our fortune to assist at. ... [T]hey were won by Meteor, with Scott for his rider; who went by the post with his hands down, the easiest of all easy half-lengths. Wiseacre certainly did the best in his power to spoil his position, and Misdeal was at one time a little vexatious. [The Sportsman, report from April 26, 1840]
Ancient Greek had akoniti "without a struggle, easily," from akonitos (adj.), literally "without dust," specifically "without the dust of the arena."
type of copper penny, 1839, American English, from red (adj.1) + cent. Pure copper pennies were issued 1793–1857, then replaced by ones of copper-nickel and, after 1864, bronze. The old cents were disused, but the phrase remained colloquial as a mere emphatic of cent, usually in the negative (don't have a ... not worth a ...). "Red" has been the color of copper, brass, and gold since ancient times.