College students, multiple adults = multiple applications?

[Susan H.]

My rental is within a mile of the university, and I previously had students apply with no income but statements that parents would pay. (This is common in this town.) I didn't have to address that issue then because the first applicants (an MD and a chef) qualified. Those tenants purchased a home and are moving out in late July. Based on what I've observed, most rentals this close to university are inhabited by multiple people, many of them students. I'll note my town has an ordinance that no more than 3 unrelated people can occupy a residence. 

My three questions:

1) Should I require each adult to complete an individual application, with that application including a section to list other adults who will be residing there?

2) And does each person pay for a credit/background check?

3) How do you handle it when tenants' parents intend to pay the rent but won't occupy the premises?

Many thanks for all comments and suggestions!

~Susan