The husband of your niece is your niece's husband. The English language and the major English-speaking cultures of the world do not have a relationship term for that person and do not consider you to be related to him.
Your husband's niece is also your niece.
The English language has no special term describing a relationship between you and your niece's husband. You would call him "my niece's husband" and he would call you "my wife's aunt" or "my wife's uncle," as the case may be.
The daughter of your husband's brother is his (and your) niece. Her daughter is his (and your) great niece.
Your husband's great niece is also your great-niece in law, so your great niece would be great niece in law to your husband.
Your niece's brother is your nephew, not her husband.The English language has no special term to for the husband of a niece. If you want to refer to him without using his name, the best you can do is "my niece's husband," or "my sister's (or brother's) son-in-law."
The daughter of your husband's brother is his (and your) niece. Her daughter is his (and your) great niece.
Your husband's niece is your niece, too. You and your husband are her aunt and uncle. Your brother is not related to a niece of yours who is the daughter of your husband's sibling.
Nothing. You may choose to call him "my niece's husband", "my nephew in law" (but that's pushing it) or by his name.
The daughter of your husband's brother is your niece.
either your niece's husband, or your nephew, or your nephew in law, etc
If you are a female you could be talking about yourself. You could also refer to a sister this way. This could also refer to a cousin of yours, since your aunt's husband may have nieces through more than one sibling (either his siblings or your aunt's siblings). It is not clear whether you are related to your aunt or to your uncle by blood, but it is very probably one of them and not both.If your aunt is the sister of one of your parents, then her husband (your uncle) may have nieces who are not related to you at all. These would be the daughters of his siblings.
either your niece's husband, or your nephew, or your nephew in law, etc