Consult with a local estate planning lawyer right away. Such a call can do you and your mother a lot of good. I don't think the State can foreclose on the house. But, there are some steps that you and your family should be considering at this point. Again, consult with a local estate planning lawyer for help. Good luck.
That depends on whether your dad and your mother had an agreement in place before he died. In Wisconsin, married couples can change the basic assumptions of marital property law with a written agreement. Because of your mother's situation, in this case an elder law attorney would possibly be able to advise you even better than an estate planning attorney.
The answer to your question depends on a number of factors. You should consult with a qualified attorney right away regarding the available options at this time. The rules for Wisconsin Medical Assistance (a/k/a Medicaid) qualification can be found in the Medicaid Eligibility Handbook (see link below). Before her money runs out, you may wish to explore setting up a WisPACT trust to pay for certain expenses which will improve the quality of her life.