You should move on and not worrying about calling him anything. If he's moved on with his cousin, you should remove yourself from that situation as soon as possible.
Your boyfriend's cousin's girlfriend, I reckon.
You would call your husband's cousin by name or "my husband's cousin." In the English language and culture, the cousin of your spouse is not considered to be related to you.
I think your dad's first cousin would be your first cousin, once removed.
That would probably be your cousin-in-law.
Cousin
Your cousin's son is your cousin, once removed. For example, if your cousin is a second cousin, the son is your second cousin, once removed.
Your mother's sister's daughter is your first cousin. Your first cousin is not related to you. You would call him by name, or refer to him as "my cousin's husband."
Since the cousin is from your half uncle's wife's side of the family the cousin would not be your cousin.
Well, your cousin's brother is also your cousin, so his wife would be your cousin in law.
That would be your Cousin.
cousin
Step son or not regarding your mother's cousin that would make him your third cousin.