The daughter of your brother is your niece.
The brother of a daughter in law is the son in law.
Your daughter's husband is your son-in-law. His brother is not related to you. If you need to refer to him other than by name you can say "my daughter's brother-in-law," or "my son-in-law's brother."
You call him your nephew. (pronouced nes-few)
The daughter of your brother or sister is your niece.
your nephew or neice
Your father's brother's son is your first cousin and your daughter's second cousin.
Use of their name is appropriate. If you have to explain their relationship, they would be your son's wife's brother, or your daughter-in-law's brother.
It would be your son. You gave birth to your daughter right? And then along the way came a boy. So your husband's daughter's brother would be your son. If your husband was previously married and your husband's daughter's brother is not your genetic son, then he would be your stepson.
Your brother's son or daughter is your nephew or niece respectively.
No, your son-in-law is married to your daughter and his brother is not your son-in-law, but simply your son-in-law's brother or your daughter's brother-in-law.
Your brother's son is your nephew. So his daughter would be your grand niece.
Your father's brother's son's daughter is your second cousin.