Certainly. Why would anyone think otherwise?
Yes, your first cousin twice removed is still related to you.
Yes.Not only can you, you are so related and cannot become unrelated to your first cousin twice removed.
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.
Your first cousin's grandsons are your first cousins, 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 grandmother's first cousin is your first cousin, twice removed. Your grandmother's second cousin is your second cousin, twice removed.
Your granddaughter and your first cousin are first cousins, twice removed, to each other.
The child of your first cousin twice removed is your first cousin thrice (three-times) removed, or your second cousins, once removed.
The nephews of your first cousin once removed, like the children of your first cousin once removed, are your first cousins twice removed.