Your cousin's daughter is your first cousin once removed. Your daughter and your cousin's daughter would be second cousins.
Second cousins
They would be cousins.
Your relationship would be that of cousins.
They would be second cousins.
Your 1st cousin's granddaughter would be your daughter's niece.
She has no relationship with your step-daughter. They do not share a common ancestor. If you adopt her, they would become second cousins once removed.
Your son and your nephew are first cousins to each other. Their daughters are second cousins to each other.
Cousins
Either they are second cousins or technically not related at all. Your cousin's niece would be one of her siblings' children, in which case it would one of your cousin's daughters, or her spouses' niece, in which case there is no blood relationship, but most families would refer to them as a cousin.
Your nephew and your daughter are first cousins.
You and the daughter of your father's first cousin are second cousins to each other
You are First Cousins