You can not unless he is unfit.
Emancipation is a matter for the courts and for the person (people) who do have legal custody of you. As your cousin does not have custody, you cousin has nothing to say about whether you can be emancipated.
It is your cousin also
They would be a cousin once removed.
A minor can not move anywhere without parental consent.
your 5th cousin
He is your cousin
cousin
your 2nd cousin, or maybe your 2nd cousin once removed.
The daughter of your father's first cousin is his first cousin, once removed, and your second cousin.
Your first cousin
cousin
cousin!