I am 55 and the parent is 80. In order to avoid tax problems, could she me to the title of her home? That way, if someday she passes on, the title of the house transfers. Or are there problems while she lives there?

What "tax problems" is she trying to avoid?

Conveying such property to oneself, along with an adult child, as joint tenants with the right of suviviorship is one way to avoid the expenses of probate. However Medicare may still be able to get the house, for a certain period after such a conveyance, if she needs to go into a retirement home.

Unless the home is very valuable, death taxes are not going to kick in.