Yes and no? It hovers in a funny gray area where most English speakers understand it and can use it, but we still think of it as being French. It hasn't been integrated as deeply as, like, "ballet" or "espionage." So when you create an artificial learning environment like Duolingo where you have to officially segregate one language from another, it becomes confusing.
Well, for me anyway. I always worry about how literal Duo is expecting me to be, because I often get it wrong.
This one was An odd one since this is a french phrase and not english. One could argue that its been used for so long that it has been absorbed into the english language in it's french form, but honestly there is no real english equivalent in my mind. Perhaps "have a good meal"
"good appetite" would be "bona apetito" without the n-finaĵo (i.e. it is merely something you are talking ABOUT). you are correct on your second guess, "bonan apetiton" with the n-finaĵo it is supposed to be understood as the grammatical direct object of a phrase that goes something like, "mi deziras al vi bonan apetiton."
I'd like to suggest a more idiomatic English translation: "Hearty appetite"! (Nowadays Americans often just say "enjoy" before a meal; sometimes you might actually hear:"Enjoy your meal." Hearty appetite is a more traditional idiom. Duo should accept it.) As some other Esperanto students have said, "good appetite" is rather awkward---at least in American English. How about in England? Any British students here? Do you folks ever say "good appetite"? I tried "hearty appetite" here but the Duo owl rejected it. Maybe we can get Duo to accept it. Have a nice day and hearty appetite!