Is it appropriate for random students to approach professors they admire?
There's nothing wrong with approaching a professor whose work you are interested in and asking for an appointment. The worst that can happen is that the professor will decline to meet with you. However, most professors (like most human beings!) will be appreciative that someone enjoys reading their work, so I'd think you're more likely to find the professor will agree than not.

That said, I would probably change what you'd say. Rather than just say "I have a few questions," I'd say "I'd like to know more about X and Y." This shows that you're serious in your request.