Yes, your brother's son would refer to you as his uncle, and you would refer to him as your nephew.
Your son would be the uncle of his brother's son.
Your Great Uncle's son would be your 2nd cousin.
Cousin
Your son is your uncle's grandnephew. Your uncle is your son's great uncle.
Your uncle would be your sons great uncle. Normally your Son would also call him 'Uncle .... '
your uncle or even half uncle but it would be no different.
She would be your niece, and you would be her aunt or uncle.
Your son would be the baby's uncle. Nobody would put such a fine point on the relationship to call your son the "Step-uncle" or "Half-uncle".
Grandmother, if your Uncle is actually the brother of your mother or father.
That would be your Cousin.
Your sister's son' son is her grandson. Your sister's grandson is your great nephew. You are his great uncle or great aunt.
We would infact, cll our sisters son your nephew and they would call you either auntie or uncle depending on your sex.