If someone is your first cousin twice removed, it means either:
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.
Your grandfather's first cousin is your first cousin, twice removed. His second cousin is your second cousin, twice removed.
Your grandfather's first cousin is your first cousin, twice removed. His second cousin is your second cousin, twice removed.
The son of your first cousin, twice removed, is your first cousin, thrice (3 times) removed.
You and your first cousin twice removed probably share more genes with each other than you do with someone you might meet at random on the street. But you cannot take genes from anyone, whether they are your first cousin twice removed or not.
Your first cousin's grandsons are your first cousins, twice removed.
Your grandmother's first cousin is your first cousin, twice removed. Your grandmother's second cousin is your second cousin, twice removed.
Your first cousin's grandson is your first cousin, twice removed. Your second cousin's grandson is your second cousin, twice removed.
Your granddaughter and your first cousin are first cousins, twice removed, to each other.
The nephews of your first cousin once removed, like the children of your first cousin once removed, are your first cousins twice removed.
The child of your first cousin, once removed, is your first cousin, twice removed, if your first cousin once removed is the child of your first cousin. If your first cousin once removed in the first cousin of one of your parents, the child is your second cousin.
Yes, your first cousin twice removed is still related to you.