Yes. Judaism and Islam prohibits the consumption of pork as it is considered an unclean animal. However, the guinea pig is a rodent, and therefore not a real pig. The second link shows that owning a guinea pig as a pet complies with kosher regulations (owning a non-kosher animal such as a real pig is contrary to Jewish law). Because the guinea pig is kosher for the purposes of pets, it should be kosher for the purpose of consumption. Of course, one must look into the method by which the guinea pig is slaughtered in anticipation of consumption.
No. Leviticus prohibits Jews from eating any mammals without split hooves who do not chew their cuds. Rodents are specifically mentioned there as unclean animals. In Deuteronomy the list of clean mammals is narrowed down further for the purposes of keeping kosher. Giraffes are kosher, but guinea pigs are decidedly not. (My source is my pocket Bible which I left in Boston, and is therefore not at my side at the moment. For further reference one can check with my employers, the Rabbinical Commission of New England, at KVH.org)
Back at my desk now, so I can say with certainty that chapter 11 of Leviticus and chapter 14 of Deuteronomy are the source texts to look at for the basic lists of kosher and non-kosher terrestrial animals, birds and fish.
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