Would your brother-in-law’s or sister-in-law’s sibling also themselves be your brother-in-law or sister-in-law? Would the spouse of your first cousin also be your first cousin?
How would this be handled in kinship systems of other cultures around the world? (Especially in very large extended families, where even the most distant kin can have family somewhere)
I consider my BIL’s wife to be my SIL. (BIL is brother of my wife).
I don’t consider my other BIL’s (sister’s husband) siblings to be a BIL or SIL of mine, though they’d be considered “kin” very vaguely. More of a kin of my kin “so you’re ok in my book” type of thing.
Granted, I don’t live in an extended family non-mobile culture.
BIL or SIL can mean different things: your wife’s siblings, or your sibling’s spouse. So it depends.
For example, your wife’s brother’s brother is also your wife’s bother.
But, if it’s your sister’s husband (who is your BIL), then it’s different. His siblings don’t have a relation to you.
Cousin in law?
My BIL’s wife and I refer to each other as the out-laws.
The relationships noted in the OP do not have specific terms in English. Whether they have terms in other languages, I do not know. (I have heard and used cousin-in-law, on occasion.)
I don’t know about the English terms, but I’d like to mention that there is a German word for what the OP refers to: A brother-in-law in the narrower sense is a Schwager in German; his sibling, who is not your brother-in-law, is referred to as Schwippschwager.
I would also use “cousin in law” for the spouse of a cousin, if that level of specificity is needed, and the folks I’m talking to would probably understand. Then again, my family is big and complicated enough that we routinely use and understand constructions like “second cousin once removed”, and we even have our own term (I know the origin, so I know it’s specific to our family) for “Cousins of cousins, to whom you’re not directly related”: We call them “Turkey cousins”.
I once met my brother’s wife’s sister’s husband’s brother. Would there be a simpler way to state that relationship than as my sister-in-law’s brother-in-law’s brother?