Why is the following sentence correct: Nobody is indispensable, is he? Why he? Which question tag can we use here?

The pronoun "he" is used here because its antecedent is "Nobody" -- both antecedent and pronoun need to be the same in person and number (in this case, singular).

If you know you're referring to a group of people who are only female (no men/boys in the group), then you should phrase this "... is she?"