Your grandfather's half brother is your great uncle.
Your sister's son is her grandson and your great nephew. Some use the term "grand nephew."
Your son would be the uncle of his brother's son.
If you have no siblings but your daughter has an uncle, he is the brother of your spouse, your brother-in-law.
your second nephew
There is no relation between you and your grandmother's cousin-in-law's grandson.
your cousin
They would be cousins, once removed.
If she's not your mother, that would make her your Aunt.
1st cousin 2x removed
You are not related as you do not share a common ancestor.
If your niece's is by your sister but the brother is by your sisters new husband & another woman there would be no blood relation. If not then he's the nephew
Hades and Zeus are brothers; Hercules is a son of Zeus and, as such, a nephew of Hades.