This sentence isn't correct. It's a colloquial expression.
It has to be:
Chiedi il perché al tuo fidanzato!
So you mean 'perche' in this sentence should be treated like an object 'the reason why' for asking. Should we generally use 'il' for this kind of 'ask why' sentences?
No, only if the "ask why" stands for its own.
Chiedi perchè ieri non è venuto. (Ask why he didn't come yesterday).
Mi chiedo il perché. (I ask why.)
Of course you can spell it "fiancé" (male) or "fiancée" (female), just like "café" or "résumé" or "soufflé." Adding the accent to the word gives it a certain je ne sais quoi.
Fiance is a word borrowed from French. In English I'd say you usually don't see it with an accent just because we don't use accent marks on our letters. But since it's a borrowed word, I don't think it would be wrong to use it with an accent.
When I heard it, I thought it said, "Chiedi perché ha il tuo fidanzato!" Uh-oh!
I answered with "you" before "ask your boyfriend why" and it wasn't accepted. Any reason why?
"Ask why of" is fine, though on the less common side and doubtless more common in text than speech. It sounds a bit formal.
You can also use "il mio ragazzo" for "my boyfriend". I'd say both are about equally common in my experience.
I have wondered this too. I have seen fidanzato used for boyfriend or fiance. Seems confusing to me.