More about kara
Patrick asks, how come kara means "China" if it comes from a Korean place name? Good question.
First of all, the specifics. (Yeah, I looked them up.) It is most likely a slight mangling of Gaya, an early-first-millennium "confederacy of chiefdoms" in southern Korea with close ties to (western) Japan.
This was the original meaning. Since Gaya was so important to Japan at that time, and since people worldwide were a lot fuzzier on geography (especially when oceans were involved), it came to mean "foreign" in general, and got applied to Chinese things too. I guess as the idea of China became more important in Japanese culture -- and since Gaya itself had long been absorbed by Silla -- "China" overtook "Korea" as the primary meaning.
As for karashishi, right, "Chinese lion" -- or actually, "Chinese beast". To expand a little on Anonymous' explanation, shishi is the native Japanese word for "meat/game" in general, so if you wanted to specify a lion in particular, you had to call it a karashishi to distinguish it from its subjects, like the inoshishi (wild boar) and the kamashishi (Japanese serow).
(Japanese Wikipedia advances the related theory that shika (deer) is from shi[shi] (meat) + ka[wa] (skin).)
language:
Interesting. The transfer from 'Korean' to 'Chinese' is parallel to the transfer of Tajik (derived from the Arab tribe Tayy) from 'Arabic' to 'Persian' (and now to 'a Central Asian group speaking a Persian dialect'), if I'm remembering correctly.