Parent death and house in name of estate

[Dan Bardar]

My dad passed away, but apparently when he refinanced the mortgage, only he was on the loan. Now my mom is living there, and she is making the payments of the remaining balance on mortgage. When the bill comes it's in the estate of my dad's name. Is there a detriment to keeping it this way and not refinancing it into her name? I don't know that she would be able to qualify on her own for the loan. She also can barely make the payments as it is. 

My second question would be if I was willing to make the payments for the remainder of the loan so she didn't have to pay it, what kind of legal docs would we need written up to make sure I would get the house when she passes. This would be a way for her to live there for the rest of her life and not have to worry about a mortgage.