You would only find amuse-gueule at high priced restaurants in the US, mostly French. Not many people would know this word in the US. As far as pronunciation, we would mangle it unless we knew French. And then it would sound very, very pretentious, unless one were at a French restaurant. Generally, a diner would say "The chef sent out a complimentary small dish." No reason to get highfalutin. I wouldn't worry about knowing this word if I were you.

Hello! I would call it an amuse-bouche, and keep the French pronunciation. When talking about cooking, fine dining, arts, and cinema in particular, there are a ton of words and phrases that have been borrowed from French that you would say as the French would, such as "mise-en-place," "mirepoix," "entreé," "montage," "avant-garde," etc. American pronunciation (if that's what you're going for) is all over the place, and there are many words that were originally French that may be pronounced differently in English, BUT in general, my advice is to pronounce it as the French would and you'll be fine! Hope that helps! :)

In the UK (I can't speak for America) we do use 'amuse-bouche' and it is pronounced the same as in French (albeit with a bad French accent!)