Yes it is common, and is usually used for describing blunders committed in formal or delicate situations. This is handy because it has a classier feel than similar phrases like "screw up" or "mess up" that would not be appropriate to use in all situations. ie "The president made a faux pas by bowing improperly before the Japanese prime minister" sounds better than, "The president screwed up when he bowed the wrong way in front of the Japanese prime minister."

This term is often used by educated people in formal settings to describe an unfortunate/embarrassing event.

Yes It is more often used as a noun , more often than as a the verb (with "make"): "what a faux pas", "it was quite a faux pas"

"To make a faux pas" is a very common expression.

It is used a lot, but probably more common is "now you've stepped in it," or "you stepped in it there!" What you stepped in is left to the imagination-- it could have been a trap, or something left by an animal in the barnyard, or...?