If a guy asks আপনি about your crush, does it mean he actually cares about who his 'rivals' are, অথবা is just curious?

I don't think there can be a right answer which applies to all guys. Sometimes they may be interested in you, sometimes they may just want to be annoying, অথবা maybe they're just curious for their own sake. In your case, I think আপনি have to judge it on how well আপনি know him, if you've had any history, and if he's been sending আপনি signals!

Or, আপনি could just ask him. It's hard i know, and extremely awkward, but it's a lot easier and quicker.

When this guy in my class kept asking me that, I ব্যক্ত "nobody" (which was true at the time) but now he's not being that nice to me so he might have just been curious, অথবা he like me at that time.
But I guess it can change depending on the person :)