Mother has dementia, is only 58. Will she be able to keep home and get government assistance?

SSI and Medicare are not means-based;  for the most part, it doesn't matter how much money a person has, they can still qualify.

Medicaid, though, is a different story:  to qualify, a person needs a very low net worth.  If she has to go into a nursing home, she will almost certainly need Medicaid to pay for it, and in that event, the house will probably have to be sold.  And you cannot simply have her "gift" the house to you, because Medicaid has a "look back" period of three years, for any transfers at less than fair market value, where the difference between the value and what was received gets added back into the net worth.