Your grandfather's first cousin is your first cousin, twice removed.
Your grandfather's second cousin is your second cousin, twice removed.
Your grandfather's third cousin is your third cousin, twice removed.
The relationship possibilities become more complex if you are talking about your grandfather's cousins who are once (or more) removed.
cousin
Your grandfather's cousin is your cousin twice removed. Her husband has no direct relationship to you.
3rd cousin
Yes, you are related to your grnadfather's first cousin. Your grandpa's first cousin is your first cousin, twice removed.
Your grandfather's great nephew is your second cousin.
Your grandfather's niece is a first cousin of one of your parents. Her son is your second cousin.
Your grandfathers' sisters' grandchildren are your second cousins.
Your daughter's grandfather's brother's son is her mother's or father's first cousin and her first cousin, once removed.
Your grandmother is first cousins with cousin. Your parent would be the second cousin of the cousin's son. That would make you second cousins once removed.
The cousin of your cousin is related to you if you share a common ancestor, such as if you are all descended from the same great grand father. If the cousin of your sousin is related to your cousin through a person to whom YOU are not related, then you are not related to the cousin of your cousin.
You are not related to your cousin's wife.
No. You are not related to the spouse of a cousin, much less the spouse's cousin.