"We write a poem."
Translation:हम एक कविता लिखते हैं।
If "we" happened to be all women, could this also be: हम एक कविता लिखती हैं।?
Yes. It should be accepted because we don't know who "we" are. We could easily be all female.
Correct, though लिखते हैं is not incorrect either, and mostly considered gender-neutral today.