What is the proper way to reach out to a university with an academic question as a layman?
It isn't really unusual, and most places will be willing to talk to you informally. You could call the department office and let them know of your interest and desire to speak to someone who might be able to help. 

Note, however, that people are busy but also schedule regular office hours so you would probably, then make an appointment with the person suggested. 

If it is just a few questions there shouldn't be any issue, but if it is more extensive, you might want to enter into a consulting relationship which would require payment.