Your sister's son and your daughter are first cousins to each other.
Grand-Nephew
Your daughter's daughter's son is your great grandson, and you are his great grandfather or great grandmother.
cousin
Your brother's son or daughter is your nephew or niece respectively.
Your sisters daygter is your neice!
You are the great aunt/uncle of your sister's son's daughter, and your sister's son's daughter is your great niece.
Your mother's son is you or your brother. Your mother's son's daughter is your daughter, or your niece. Your mother's son's daughter's mother is your wife, or your sister-in-law.
Your daughter's husband is your son-in-law.
Your nephew's daughter's son is your great-great nephew. Your nephew's daughter is your great niece.
Your son-in-law is your Daughter's husband. His family are part of your extended family but while your daughter is an Aunt (by marriage) to the child and the child is a Niece (by marriage) to your Daughter. The child is no direct relation to you.
Your father's sister is your aunt and her son is your first cousin.
If you are married to your daughter's mother, then her boy is your stepson. If you are not married, then he is no relation to you. Either way, he is your daughter's half brother.