Maybe, it will depend on your facts and whether you pass the income, assets, health, and service tests necessary to qualify for A&A. You should seek out a VSO office in your area or contact an accredited VA representative or attorney.
Check to see how your father's boat was titled. Was it in his name personally or in the name of his revocable trust? If the former, you should consider retaining a probate lawyer to help you with doing a summary administration probate proceeding. Good luck!
Yes, you can execute the lady bird deed. However, it is not necessary, since the home is already protected from Medicaid state recovery by being held in the trust. You will avoid probate too, since the home is titled in the trust.
Your mom will be able to get back on SSI, Medicaid and Food stamps after she is re-qualified to be eligible. Yes, she need to "track" or account for the spend down of the inheritance. Your mom may want to consider talking to an elder law attorney for further details.