Given that this sounds like a fairly large property, you'd benefit from establishing your mission, what you and your brand stand for, the value proposition you offer to your customers, and other important considerations.

The seller claims its approximately $15k.

I rent to college student here in NY State and an arguement has ensued over a desk between two tenants in which one said they owned it and let the other borrow temporarily and the other is claiming it was given to them.

That being said, it allows for various payment frequencies, greater customization, and e-signatures for leases.  

His negotiation was $900 for January rent, February rent and all damagesIf he does leave you have to start a small court claims (figuring out where he lives because why would he tell you if you are not sending back a deposit) for anything over.Good luck and you can make it work out.

Do I wait till the rental property is back in service to claim deductions and income?

Save, seek and maintain gainful employment (if hourly and you take time off b/c you are sick, do the paperwork to get the sick pay, so it doesn't look like you took an unpaid vacation - paperwork matters more than verbal claims made!

Anyway, my long point of this is there are many factors to your eventual revenue once you get started which include but are not limited to: Location, Beds, Reviews, Amenities, Customer Service, unique guest experience, etc. etc.. 

We recently installed a new package HVAC system for her in the property which wasn't cheap.I am wondering as her landlord and manager what I should do and also what I can do.Do I have to let her break her 1 year lease early because she is claiming a "domestic abuse" situation?

It's those maniacs that buy homes cash via quit claim deed off of craigslist that really get screwed.Make sure your property manager is a licensed real estate brokerage.Google Clayton Morris and/or Morris Invest for a cautionary tale of what not to do when buying turnkey real estateUnderstand you can not eliminate all risk, only mitigate it.