Great Great Aunt
Your great grandfather's half-sister is your great great aunt, the same as his full-sister is.
Your great grandfather's sister is your great great aunt. You are her great great niece or great great nephew, depending on your sex.
Your grandfather's sister is your great aunt.
your mother is called your mother. her dad is your grandfather. and his dad is your great grandfather. and then each parent of that you add a great. e.g. your great grandfathers father is your great great grandfather. ect.
At most, each person has: 1 Father 2 Grandfathers 4 Great-grandfathers 8 Great-great-grandfathers - etc. If there have been marriages between cousins, the number of individual ancestors may be reduced as one person fits tow or more places on the family tree.
Your great great grandfather.
Of course you are related to the great grandson of your great great grandfathers sister. You have common ancestors in your great great great grandparents. The two of your are third cousins, once removed.
He would be your great great uncle, but you could call him whatever endearing name you both prefer. my great grandfathers brother or my great uncle
What is your great-great-great grand nephew?!
my great great great great great grandfathers uncle
She would be your great grandmother
They would be 3rd cousins.