The nephew of a wife and the nephew of her husband are not considered to be related to each other. However, both are nephews of the wife and the husband, and the wife and husband are aunt and uncle to both nephews.
You can call your niece's husband your nephew or your nephew-in-law, if you like, but strictly speaking, he is not related to you.
There is no common ancestor. They aren't really related, but most families would refer to them a distant cousins.
Your husband's nephew is also your nephew, or you can call him your "nephew-in-law" if you want to distance yourself from that relationship.
The English language has not relationship name for the wife of your husband's nephew. You are not considered to be related.
Children of your siblings are nieces and nephews. Children of your spouse's siblings are still called nieces and nephews, but you are not related to them by blood.
You are not related to your niece's husband, although some would call him your nephew by marriage. But that is a relatively recent construction and not used by many. You could also call him your brother's (or sister's) son-in-law.
Some would call your nephew's children your grand nephews and grand nieces, others would call then your great nephews and great nieces.
If it is a boy then it is your nephew. If it is a girl then it is your niece.
Your nephew's child is your great niece (if a girl) or your great nephew (if a boy).
Your brother's child's children are your grandnieces or grandnephews.
You are your aunt's nephew and therefore also her husband's nephew. Her husband is your uncle.
either your niece's husband, or your nephew, or your nephew in law, etc
There is no special term in the English language to describe a relationship between you and your nephew's wife. To her, you are just "my husband's uncle." If she has children with your nephew, they will be your great nephews and great nieces and you will be their great uncle or great aunt.
The children of your husband's sister are your nieces or nephews, and you are their aunt, just as he is their uncle.
either your niece's husband, or your nephew, or your nephew in law, etc
The children of your husband's siblings are your nieces or nephews. Their children are your great-nieces or great-nephews.