Apparently "party" and "celebration" are different. How would you say "party" in French?
This doesn't seem like a sentence that anyone would use in English. I would only say "What is the date of the celebration?" or "What day is the celebration?"
"Fête" is actually used to refer to the French (catholic) observance of a person's "saint's day", also called "name day". The idea is that each day in the year is associated with a different saint. For those who observe this practice, it is a special celebration for the day associated with the same name as yourself. https://en.wikipedia.org/wiki/Calendar_of_saints It might be mistaken for a birthday, but it is actually a saint's day.
Indeed, "Bonne fête à toi" is something French Canadians might sing at a birthday, and the following Wiktionary entry includes "(Canada) birthday" as one of the definitions of "fête":
"Fête" for this usage is probably a result of the confounding of the name-day celebrations mentioned by n6zs with birthday celebrations, particularly since French-speaking Canada is traditionally very much Catholic.
But "anniversaire" would still be valid for "birthday" in French-speaking Canada, and strictly speaking might be considered more correct. I have a Canadian dictionary that lists "birthday" for only the "anniversaire" entry in the French-English portion, not for the "fête" entry, but in the English-French portion it lists "[saint's day] fête" for the "birthday" entry.
But keep in mind that "fête" can also be just a celebration in general.
Surely "day of the party/celebration" should be okay? In English "day" is used for "date" very often. (IE, "what day is the party" could have an answer like "thursday" or "the 9th")
The issue is that the French question is being posed in a precise way, not in a way that would have both of those two options for answering, and so that's how it should be translated, presumably.
When I was in Quebec my friends referred to fête as a party. I used party instead of celebration is that wrong?
It's okay according to Collins:
What you're asking about is called "elision" or "contraction", not "conjugation".
In French, elision doesn't take away consonants (like the two ls in "quelle"), so you would never see it work as you suggest.
You can read more about it at these sites: