"Fish doesn't live in deserts" - is this part of an exercise question correct?

I came across this question in an external exercise book for a secondary school textbook: 2

Shouldn't we use "A fish" or "Fish don't" to make the sentence grammatical and sound natural?

Yes, you are right in thinking that question 8, with it following the ellipsis, is wrong. It should read

Fish don't live in deserts, ... they? (Answer: do)

or possibly

A fish doesn't live in the desert, ... it? (Answer: does)