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 first cousin's second cousin may be your second cousin as well, or may not be related to you at all.
Your grandmother's second cousin is also your second cousin, but twice removed. The twice removed means the number of generations between you. Your mother's first cousin is your first cousin once removed. If your mother's first cousin has children, they are your second cousins.
Asking about your second cousin's cousin's cousin is asking about a complex but poorly defined relationship. Are the cousins of the second cousin his first cousin, second cousin, fifth cousin twice removed, or something else. It is likely that a cousin's cousin's cousin is not related to you at all. It is also possible that your second cousin's first cousin's first cousin is also your second cousin.
Your mother's first cousin is YOUR first cousin, once removed. The child of your mother's first cousin is YOUR second cousin.
Your mother's first cousin is your first cousin, once removed.Your mother's first cousin, once removed is your second cousin.Your mother's second cousin is your second cousin, once removed.
Your first cousin's child would be your second cousin
The child of your first cousin is your first cousin, once removed.The child of your second cousin is your second cousin, once removed.And so forth.
Your parent's first cousin is your first cousin, once removed. Your parent's second cousin is your second cousin, once removed. Your parent's first cousin once removed may be your second cousin.
Your grandfather's first cousin is your first cousin, twice removed. His second cousin is your second cousin, twice removed.
Your second cousin's son (or daughter) is your second cousin, once removed.
Your daughter's second cousin is your first cousin, once removed, but only if your daughter's second cousin descends from your aunt or uncle. If your daughter's second cousin descends from your spouse's aunt or uncle, then your daughter's second cousin in not related to you.
Your dad's first cousin is your first cousin once removed. Your dad's first cousin's children are your second cousins. Your dad's second cousin is your second cousin, once removed. Your dad's second cousin's children are your third cousins.