You and your second cousin, once removed, are members of the third and fourth generations of descendants from an ancestor that you have in common. If you are the member of the older (third) generation, then your common ancestor is your great grandparent. If you are the member of the younger (fourth) generation, that common ancestor is your great great grandparent.
If you are in the third generation from your common ancestor then one of the parents of your second cousin, once removed, is your second cousin. The other is not related to you.
If you are a member of the fourth generation from your common ancestor, then one of the parents of your second cousin, once removed, is your first cousin, twice removed. The other parent is not related to you.
The granddaughter of your parent's first cousin is your second cousin, once removed.
The granddaughter of your parent's second cousin is your third cousins, once removed.
And so forth.
Assessing your relationship to first, second or other of your parents cousins who are once, twice or more removed from your parents is a more complex process, with two possible answers in all cases.
The children of your first cousin once removed are your second cousins if your first cousins once removed is your parent's first cousn.
The children of your first couisn oncer removed are your first cousin's twice removed if your first cousin once removed is the child of your first cousin.
Your second cousins are the children of your parent's first cousins.
The daughter of your first cousin, once removed, is your first cousin, twice removed.
Your parent's first cousin is your first cousin, once removed.
You and your first cousin have one or more grandparents in common. One of your parents is the brother or sister of one of your first cousin's parents.
If your second cousin's mother is related to you, she is your first cousin, once removed. Remember that one of your second cousin's parents will not be related to you.
Your grandfather's niece is the first cousin of one of your parents, and your first cousin, once removed.
Your uncle's first cousin is also your parent's first cousin, and your first cousin, once removed - if your uncle is the brother of one of your parents. Sometimes your uncle is the husband of your parent's sister. Then his cousin in not related to you.
Your uncle's first cousin is also your parent's first cousin, and your first cousin, once removed - if your uncle is the brother of one of your parents. Sometimes your uncle is the husband of your parent's sister. Then his cousin in not related to you.
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.
Your uncle's first cousin is also the first cousin of one of your parents. So this is the same as asking how are you related to the daughter of you parent's first cousin. Your and the child of your parent's first cousin are second cousins to each other.
Your first cousin is the child of your parent's sibling. Your second cousin is the grandchild of your grandparent's sibling. So your first cousin is more closely related to you than your second cousin and is "first in line" if you leave no living children, grandchildren, parents or siblings.
Your uncle's first cousin may also be the first cousin of one of your parents if descended fromyour great grandparent. In that case, your uncle's first cousin would be your first cousin, once removed. On the other hand, your uncle's first cousin may be related to that parent of your uncle who is not descended from you great grandparent. In that case, your uncle's first cousin is not related to you.
Everyone has two sets of grandparents - the mother's parents and the father's parents. You and your 1st cousin share one set of grandparents because one of your cousin's parents is a sibling of one of your parents. So, yes, your first cousin has a grandmother who is also grandmother. That cousin also has a grandmother who is not your grandmother, and, in fact, is not related to you at all.
Your sister's cousin is your cousin, too, unless you and your sister are really step siblings with different parents. Then your sister's cousin is not related to you.
Assuming both children are on the same side of the family, your child's first cousin is a second cousin to your first cousin's child. Your child is also a second cousin to your first cousin's child. Your child can have first cousins who are not related to your first cousin and thus not related to your first cousin's child.