I'm wondering if some one can help with an explanation about why a Hotel has many rooms with tax lien on auction? 

Some might not be livable at purchase but 5k still seems cheap unless there is something off with the data. maybe the prices were reduced on unlivable properties due to back taxes being part of the deal for the purchase.

Hmm, the title company said they couldn't determine the amount, only that there was an agreement to the terms of another agreement... like a notice for hoa responsibility tells you they're responsible but not how much is owed.

Here are the specifics: our current property is worth 360k roughly; we owe 120K on it.

My lawyer suggests in a situation like this that I give them a notice that I am the new owner and that as of a certain date they owe market rent of $X,XXX.

It can be done ethically, but you need safeguards to confirm mortgage & possibly property tax payments made on-time, as well as insurance with you protected.- Also, you need a legal way to take back the deed if buyer defaults!

As for numbers, I currently owe $86,151 on the mortgage, and on Zillow it is listed at $143,600 but the numbers seem to be inflated on that site.  

@David R Pustelnik recommend you first focus on raising the rent for the first time in 10 years.By the way, how much have your property taxes and home insurance gone up since this tenant moved in?

I assume they collect a proration every month for property tax?

If she gifts the home to you, you inherit he cost basis and owe all the taxes.