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Your father's third cousins are your third cousins, once removed.
If your grandmother and his grandmother were first cousins, then you and he share a great grandparent and are third cousins.
Your third cousins and your children are third cousins, once removed. Your first cousin and your children are first cousin, once removed.
Your third cousins and your children are third cousins, once removed.
Move down to the row that corresponds to the relationship of the second person to the common ancestor.
The children of your mother's first cousins are your second cousins. Taking that further, to sexual activity, is another matter, but fourth cousins are not very closely related and very few groups would think anything of a marriage between fourth cousins. I'd okay it with your cousin and her boyfriend, and your cousin's boyfriend and cousin's boyfriend's sister's parents first.
The children of your mother's second cousins are your third cousins. Fourth cousins are people who share a common great-great-great grandparent. Your father's first cousin's children are your second cousins.
At least 20 states in the United States allow first cousins to marry, and most states allow the marriage of a person to a first cousin once removed.
A second cousin is even more distantly related than a first cousin once removed, and I know of no legal bar to second cousin marriages.