Genetic factors do contribute substantially to the likelihood of developing Bipolar disorder, so yes, there is a chance you could "get it". However, there's a chance you could get it even without any relatives who have it; the genetics are not well understood (no one is even sure which specific genes are involved, so you can't realistically even test for it).
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 mother's First Cousin is your First Cousin, Once Removed. The child of your mother's First Cousin is your Second Cousin
Your mother's first cousin's son is your second cousin. Your mother's second cousin's son is your third cousin. And so forth.
Your mother's first cousin is your first cousin, once removed. Your mother's second cousin is your second cousins, once removed. Your mother's third cousin is your third cousin, once removed. The potential relationships become more complex if your are talking about your mothers cousins once, twice or more removed.
Your mother's first cousin is your first cousin once removed. Your mother's second cousin is your second cousin once removed. If you are talking about your mother's first cousin once removed, you may be first cousins twice removed or second cousins, depending on the specifics.
Your mother's first cousin's child is your first cousin, once removed.Your mother's first cousin's child is your child's second cousin.
Your mother's first cousin's daughter is your second cousin.
Your mother's cousin's son is your second cousin.
Your mother's first cousin is your first cousin, once removed
No, your mother's first cousin is your first cousin once removed. Her second cousin is your second cousin once removed. Your mother's sister is your aunt.
The child of your mother's first cousin is your second cousin. The child of you mother's second cousin is your third cousin.
Your mother's first cousin is YOUR first cousin, once removed. The child of your mother's first cousin is YOUR second cousin.