the daughter's cousin
Yes, it should be, it is not considered incest because it is not by blood. You are marrying your aunt's HUSBAND'S daughter.
First cousins, twice removed. Aunts daughter is your cousin. Aunts daughters daughter is cousin once removed Aunts daughters daughters daughter is cousin twice removed.
Your aunt is either your parent's sister or the wife of your parent's brother. If she is your parent's sister, her husband, his sister and her daughter are not related to you. If your aunt is the wife of your parent's brother, then her husband's sister is your mother (and her daughter is you or your sister) or she is another of your aunts (and her daughter is your first cousin).
yes
Your first cousin.
Her aunts/uncles daughter.
great nephew
They'd be your cousin.
The daughter of your husband's brother is his (and your) niece. Her daughter is his (and your) great niece.
no you have to say: my husband, my daughter and i ....
The daughter of your husband's brother is his (and your) niece. Her daughter is his (and your) great niece.