Your father should consult with an attorney in the area where he lives for specific legal advice regarding what his options are in these circumstances. He can search for an elder law or estate planning attorney.
All of the options you mention can be possible means of Medicaid Planning, but it's not possible here to discuss all of them in detail as they apply to your situation. That's why it's important to contact an elder law attorney.
A life estate is a gift of the remainder interest (post-death interest) in the home, therefore it is subject to the five year lookback rule that applies to Medicaid applications. It may also create some capital gains issues for the recipient of the remainder interest.
If a parent transfers or devises (in a will) the residence to a child who cared for the parent AND the parent would have needed to go to assisted living or a nursing home if that care had not been provided, the transfer to the child MAY be exempt from the Medicaid Estate Recovery Act. However, as with your other questions, the answers are very dependent on your particular circumstances and only a qualified attorney can advise you on which options suit you and your father best.