It will depend on whether you share a common ancestor. Your aunt's niece could be your sister or a first cousin. There is also a chance that there is no relationship at all. Do you share a grandparent? If the answer is yes, you are related. If no, you are not related.
great nephew
A nephew is a cousin to his aunt's son.
The English language does not contain a specific term to describe a relationship between you and your nephew's wife. The culture does not consider her to be related to you. Most aunts and uncles would merely call her "my nephew's wife."
Jack and Jill
Your parent's sisters are your aunts. You are their niece if you are a girl, or their nephew if you are a boy.
I believe they would be great aunts or great uncles.
Your are related to some of your first cousin's aunts and not to others. The aunts of your first cousin to whom you may be related are your mother and her sisters or your father's sisters. One of the parents of your first cousin isn't related to you, but married into the family. Anyone of your cousins aunts who are related to that person would not be related to you.
Niece is to nephew as sister is to brother.
yes
Your nephew's first cousin may or may not be related to you, depending on how the cousin is related to your nephew. Your nephew's cousin may be your child, or the child of one of your brothers or sisters. Your nephew is related to you by being the son of your sibling. That sibling has a spouse who may also have borthers and sisters. The children of any of those brothers and sisters are also your nephew's first cousins, but are not related to you.
Your nephew's son isyour great nephew. You are his great aunt or great uncle.
In-laws are not related.