If you are inquisitive that means you love to inquire; you’re always asking questions. Don’t become a private detective if you don’t have an inquisitive personality.
The old word for question is query, which you can hear in inquire, which means to ask questions. That toddler always asking “why?” is going through an inquisitive stage of development. If someone throws relentlessly hard questions at us, we might call it an inquisition. If your daughter brings her boyfriend home to dinner, be gently inquisitive, but try not to turn it into an inquisition. You'll just make him nervous.