Yes you can marry her. She has no blood relation to you. She is just the niece of your brother's wife from her side.
It is no different than if two cousins married two women who were sisters.
This is an unclear and rarely used phrase - "your brother's daughter through marriage." If your brother married a woman and they had a daughter, the daughter is "your brother's daughter through marriage" since the one followed the other. That daughter is your niece. If your brother married a woman who already had a daughter from a previous relationship, that daughter is your niece only if your brother adopted her. If he did not adopt her, you are not related. However, you can treat her as your niece if you want to.
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.
There is no relationship, they share no common ancestor.
Your sister's husband is your brother-in-law. The daughter of his sister is his niece, and your sister's niece, but is not related to you. Assuming the child was born to the woman before she met your brother, the daughter of the woman whose brother married your sister is not related to you.
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.
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.
No, you do not share a common ancestor.
Your wife's brother's daughter is her niece and your wife is her niece's aunt. Although you have no genetic relationship to your wife's niece, by convention your wife's niece is considered to be your niece and you are her uncle.
9. He was the 5th.
The English language has no special term for the brother of the woman who married your son.
Abraham married his half sister Sarah. Gen:20:12: And yet indeed she is my sister; she is the daughter of my father, but not the daughter of my mother; and she became my wife.
Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.Cleopatra's daughter married king Juba II of Mauritania.