Good questions you pose, reflecting significant research and considered application to the facts you address. The answers, I'm afraid, depend on so many things like the terms/conditions of the applicable documents as applied to a more full description of the operative facts, upon which we can conduct a comprehensive analysis. Feel free to contact me directly if you would like to further discuss. There is no obligation to you. If not, best of luck.

LI means Life Interest.

You can sell the place; have your uncle's life interest valued and compensate him when the property is sold.

Affidavit is a valid transfer.

A notarized affidavit is not a valid transfer of an interest unless it meets the requirements of a deed or meets the requirements of a valid will. Assuming that it is not a valid deed or will, you will have to probate your mother's estate and the owner of her 1/3d interest will whoever inherits under her estate. As for the life interest, you can wait until your uncle dies or have your uncle join in the deed. If your uncle is not competent, you will need a guardianship to do this. However, if you sell your uncle's interest, the value of his interest may go to pay for his nursing home costs. It appears that your interest in the real estate at present is 1/3rd of the value after the termination of the life estate. This means that your interest is worth considerably less than 1/3rd of the value. However, if you wait for your uncle to die, then your interest will be 1/3d of the value. You will get more money if you wait and you won't have to pay to have a guardianship of your uncle.