Your great grandfather's great niece is the grandchild of his brother or sister. That makes her the second cousin of your mother or your father, and therefore your second cousin, once removed.
Your grandfather's sister is your great aunt.
Most likely they would not be related to you
The son of your great niece is your great great nephew.
For clarity, lets call your great great grandfather's niece "the niece". The relationship sequence: (1) The niece is the daughter of your great great grandfather's sibling (2) The niece is a 1st cousin of one of your great grandparents (3) The niece is a 1st cousin once removed of one of your grandparents (4) The niece is a 1st cousin twice removed of one of your parents (5) The niece is your 1st cousin three times removed
Your niece's son is your great nephew. You are his great aunt or great uncle.
Your great grandfather's sister is your great great aunt. You are her great great niece or great great nephew, depending on your sex.
Your niece's husband's daughter is also your niece's daughter and therefore she is your great niece. You are her great aunt or great uncle, depending on your sex. If your niece's husband's daughter is from a previous marriage, and so not also your niece's daughter, you are not related to her. Of course, if your niece adopts her, then she is your adopted great niece. If your niece married her husband while his daughter was very young and everyone has been treating her as your niece's daughter, then you can call her your great niece if you want, but that does not change the fact that you have no common ancestors and therefore are not related to each other.
maybe
Your grandchildren and your great niece are second cousins to each other.
Your grandson and your great great niece are second cousins, once removed, to each other
You and your grandmother's great niece are second cousins.
You are great great aunt to your niece's grandchild. Your children and your niece's grandchild are first cousins, twice removed.