A: It is the part of the instrument that is called the “embouchure”.

Q: “What is the mouthpiece?”

Hmmm. I would have wanted to answer “What is the mouth formation used when playing a wind instrument?” or some such thing. (I probably would just have said, “What is the mouth?” knowing that didn’t quite say it all.) But I looked it up and, sure enough, the dictionary gives “mouthpiece” as a definition. But … whew! … it also includes “the adjustment of a player’s mouth to such a mouthpiece”.

I can breathe easy.