Yes. Your first cousin twice removed is either the grandchild of your first cousin (and you have a common ancestor in your grandparent),OR is the first cousin of your grandparent (and you have a common ancestor in your great-great grandparent). The common ancestor is the same person in either case, but is called differently depending on whether the relationship of "first cousin twice removed" is looked at from the point of view of the member of the older or younger generation. See the releated link for a fuller explanation.
yes
Yes, your first cousin twice removed is still related to you.
Your first cousin's child is your first cousin once removed (one generation removed).Your first cousin's grandchild is your first cousin twice removed.
Your cousin's child would be your first cousin once removed. So, your cousin's adopted child would be your adopted first cousin once removed?
Your grandmother's first cousin is your first cousin, twice removed. Your grandmother's second cousin is your second cousin, twice removed.
Your mother's first cousin is your first cousin, once removed. Your mother's second cousin is your second cousin, once removed.
Your first cousin's grandchild is your first cousin, twice removed.
Your mother's first cousin is your first cousin once removed.
Your grandfather's first cousin is your first cousin, twice removed.
All of your cousin's descendents are related to you. Your first cousin's grand chid is your first cousin, twice removed.
Of course, your first cousin's child is related to you; you have ancestors who are also ancestors of your cousin's child. Your first cousin's child is your first cousin, once removed. Your second cousin's child is your second cousin, once removed.
There are two ways you can have a first cousin, once removed.If your first cousin, once removed, is the first cousin of one of your parents, then the daughter is your second cousin.If your first cousin, once removed, is the child of your first cousin, then the daughter is your first cousin, twice removed.