I'd like the following partial answer explained further.
If you think your mother may not be able to wait that long before needing nursing home care, then a combination of an outright gift to her children and a purchase of a "Medicaid annuity" can protect roughly half of her assets. This technique can be done immediately, even if the parent is already in a nursing home.
A Medicaid annuity is a special type of annuity that is irrevocable, non-transferable, immediate, and fixed to equal monthly payments. With the right type of annuity, it is non-countable as an asset for Medicaid purposes, and the purchase is not considered a gift that might otherwise cause a disqualification period.