Re: joint possession/separate possession
I can see this developing into a long string...
1-We met they and their cousins' friends. This is not correct. Take "and their cousins" out of the sentence, and the remainder should still make sense. In this case it doesn't.
2-We met friends of them and of their cousins. This is fine, and tends to reflect your option "b". However,it does not absolutely rule out that some or all of the friends were shared. A comma after "them" might strengthen the separation of the two groups.
3-We met their and their cousins friends. This is also fine, so long as you remember to include the apostrophe after "cousins" to indicate the possessive. It tends towards option "a", but two groups cannot be ruled out.
4-We met their cousins' friends and theirs. This is fine, and tends towards option "b". Again, however, the other option cannot be ruled out.
In all of the above, we are assuming that there is more than one cousin. If there is only one cousin, then Nos 1, 3, and 4 should be "cousin's", and No 2 should be "cousin".
Finally, let me emphasise once again that none of these sentences make it absolutely clear whether these friends are separate or shared. To do so, you would have to say something like: "We met their friends, and we also met some of their cousins' friends".
I'm not a teacher of English, but I have spoken it for (almost) all of my life....