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.

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?

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

Looking my insurance policy it mentions that I can opt for settlement under Actual Cash Value vs Replacement Cost. 

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.

Hey, I’m looking to connect and network with private individuals who lend money on real estate deals. Do you know of any good websites where I can post my deals?

I have to evict using the landlord tenant route, but I don't know which reason to choose.