Unless I hear from the tenant as to when the rent is coming, we'll serve a pay or quit notice as soon as the grace period has expired.

I’m in an exciting period in my life.

That is a must for success, period.

But if the hospital is poorly run and the travel assignment is rough, chances are the nurse won’t try to extend their contract there.  

The rental period after you move out of your PR is not considered non-qualified use.

And if you’ve never done this before I would caution getting a property from a wholesaler because you have no option period no inspection and no one in your corner.

Meanwhile, the period for the offer we got expires in just a few weeks. 

If you do that then you would need to to wait for the seasoning period to end, which is at least 6 months, but even after that point, if you have done nothing to the home to increase its value or the market value has not increased significantly, you won't have any equity to cash out with on the refinance.   

Her home is estimated to be around $240k and she owes $37k.I'm estimating repairs to be around $10k and I currently have $50k availableI am trying to think of a way that makes sense for me to purchase the house and take care of the repairs so she doesn't have to worry about coming up with any other money, while at the same time not tying up all my money for a long period of time. 

Also, I would recommend periodic (3-6 months) walkthru of the property to validate safety and ensure tenant is following the rules.