What is their policy for dealing with evictions?

Most HOAs have a policy whereby they notify of an infraction and give a certain period of time for resolution and then they fine... is that not the case here?

If so, you have to fix safety issues, or whatever issues are called for by the terms of the lease. 

We're also each getting umbrella policies for protection.

You may also want to require that they add you as an additional insured to their policy with 30 day notice of cancellation. 

Some of which include: Debt ServiceInsurance (proper STR insurance - not a standard fire policy)Taxes (both normal property and STR taxes)HOA DuesVacancyCAPEXElectricity, Cable, InternetFurnitureSheets, towels, etcCleaning/maintenance Gardening/lawn-care Etc.Im sure I missed a few - but you get the point.

I'm a little concerned about the area for safety reasons.

In reality regardless of you wanting to not rent to students or not; These checks (or policies) should be in place. 

My agreement with my PM is silent on the topic of late fees, covered by this generic clause: b.Operate the property according to good business practices pursuant to a general overall plan as established from time to time by Manager and OwnerI normally e-mail my PM asking what their policy is and go from there.I've had to focus on the really big things and let the minor irritations slide.  

Just watch for the specific counties policies in Airb renting versus regular/long term renting and be sure you get your rental license/certificate.