The first cousin of your mother's first cousin may be your second cousin, or may not be related to you at all. It depends on how he cousin relationship in your mother's generation is structured.
Your mothers sisters Granddaughter is your second cousin
The relationship to you would be your cousin !
She is your third cousin.
2nd Cousin
Your mother's aunt's son is her first cousin and your first cousin, once removed.
2nd cousin, but if it's your Dad's 2nd cousin... then your relationship with that cousin would be a 3rd cousin.
You are their aunt or aunt by marriage.
No. It's prudent to not be in a relationship with a first cousin.
Your niece would be your mothers granddaughter.
If your uncle's cousin is also the cousin of your parents, you are first cousins once removed. If not, there is no relationship as you do not share a common ancestor.
second cousin
Your cousin. You are that person's second cousin.