The best explanation I've found (and general guidance on introducing family members) has come from the Coffee Break Italian series:
Their podcast is free to listen to and does a great job covering the basics. I've also found it very helpful for pronunciation!
hmm, I put "she is not my cousin" at first, and when it marked me wrong it told me the correct answer was "it's not my cousin" - but then when I gave that as the answer, I was marked wrong again...
It absolutely should be accepted. E.g. if you are looking at the photo and you are pointing at a person at this photo, you can say "it is not my cousin". I don't see how else you can say it in Italian, thatn "Non è mio cugino"