Yes. The grandparents of one are the great-grandparents of the other.
Yes. They are your First Cousins, twice removed.
Your Father's first cousins are also your first cousins, once removed.
They are out of synch by a generation. They would be first cousins once removed.
You are first cousins once removed to each other.
You and your first cousin's children are first cousins once removed. Your children are their second cousins.
The nephews of your first cousin once removed, like the children of your first cousin once removed, are your first cousins twice removed.
Yes, being cousins means that you are related.
Your son and your niece are first cousins. Her daughter and your son are first cousins, once removed.
They are out of synch to a common ancestor by one generation. That would make the first cousins once removed.
First cousins three times removed.
The English language has no special term for the cousin of a cousin. Either that person is related to you, and so is describable by that direct relationship as some sort of cousin (or a sibling), or is not related to you.
No, your cousin's daughter is your cousin, once removed. So your first cousin's daughter is your first cousin, once removed, and your second cousin's daughter is your second cousin, once removed.