Since the ancestors of your great uncle's wife are not related to you, the first cousin 14 times removed of the wife of her 15th great grand uncle is not related to you, nor you to him.
Your grandfather's brother is your great uncle. The wife of your great uncle is your great aunt.
Your sister's son is your nephew. Your uncle is your nephew's grand uncle or great uncle.
Your grandmother's nephew would be your parent's first cousin. They would be your first cousin once removed. Since the child of your cousin is a generation away from you they are the once removed.
Your great uncle's grandchild is your second cousin. (Your great uncle's child is your first cousin, once removed and your parent's first cousin.)
Your great uncle's granddaughter is your second cousin.
Your first cousin's great grand uncle (also called great great uncle) could be your great great uncle, or could be unrelated to you. The same applies to the great great uncle of your second cousin. For other cousin relationships the possibilities become more varied, but always include not being related to you at all.
Grand Aunt or Grand Uncle depends what gender you are.
The child of your great uncle is the first cousin to your mother or your father, and is your first cousin, once removed.
You and your uncle's great grandchild are first cousin, twice removed.
Your grandmother's brother is your great uncle. Your great uncle's son's great granddaughter is your great uncle's great great granddaughter. Your great uncle's great great granddaughter is your second cousin, twice removed, and is your daughter's third cousin, once removed.
Your uncle's great granddaughter is your first cousin, twice removed.
Your uncle's daughter is your first cousin. In the English language, it does not matter whether the uncle is a maternal uncle or a paternal uncle. All the children of your aunts and uncles are your first cousins.