Your grandfather's niece is the first cousin of one of your parents, and your first cousin, once removed.
Most likely they would not be related to you
Your grandfather's sister is your great aunt.
Your grandfathers' sisters' grandchildren are your second cousins.
Your father's nephews and nieces are your first cousins.
Your grandfather's niece is a first cousin of one of your parents. Her son is your second cousin.
No. Your wife's niece is also your niece, but the husband of the niece is not related to you or to your wife.
Your father's niece is your 1st cousin.
Your sister-in-law's niece is not related to you because you have no ancestors in common. ----- The above answer is true, but by marriage, that niece would also be your niece or your own daughter. This is because your spouse is blood/sibling related to his/her sister (your sister-in-law).
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.
No
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 grandchild and your niece are first cousins, once removed.