My lease requires professional carpet cleaning, which would cost more than $500 for a home of that size.Yes, it's reasonable to reduce the cost because she was such a long-term tenant.

Quote from @Dan Mcguire: One reason not to invest, is not to lose money.

Mainly the "self sufficiency test". 

We appreciate your support and understanding during this challenging time.A medical note attached simply says "1 year leave from school for medical reasons"Please advise on what is the best recourse in handling a situation like this?

Does this approach seem reasonable, or am I undervaluing the property?

It is also for that very reason that you should be wary about going in as I do feel that the Pittsburgh has gone pretty high up in it's property values. 

Quote from @V.G Jason: The first and foremost reason most people don't work with BP agents is cause 99%  of them are absolute trash.

Loan terms seem reasonable.

One of two reasons most likely:1.

There is a case for buying well-located solid assets that produce immediate current cash flow at reasonable leverage.