"Extraordinaire" is a French word, but we sometimes borrow French expressions to make our writing seem classier or more stylish. It can also make the writer sound pretentious, so gauge your audience before you use it. ;) As far as using "extraordinaire" goes, use the French word-order: a teacher extraordinaire.

"Extraordinary" is a regular, and frequently used English adjective and it goes before the noun. "Extraordinaire" is not rare, but it's not frequent, either. It is almost more of a loan PHRASE from French than a loan word and it follows the French word order: "X extraordinaire." We think of it as French, as we think of "bon appetit" or "a la mode" or "haute cuisine" as being French, and we pronounce them all with a rough approximation to French pronunciation. In contrast, we rarely think of "garage" or "envelope" or "role" as French. Although one dictionary I checked simply defines "extraordinaire" as "extraordinary," I don't agree. To begin with, you can only use it when paying a compliment to a person. And it only means "extraordinarily good," not extraordinary in any other way. You could say "Saturn is an extraordinary planet" but you would never say "Saturn is a planet extraordinaire." And when applied to a person, I think it is a stronger word than extraordinary. It is almost as if you are suggesting that this person is so extraordinary that there are no words in English strong enough to express it.

Correct. I think it's a loan word from French, and in French the adjective generally comes after the noun. So it kind of defies typical English sentence structure.