Learn Dutch: Er zit niets in de zak, maar niemand gelooft mij. - There is nothing in the bag, but nobody believes me.

Both are negative indefinite pronouns. Niets means "nothing" and is used for things, while niemand means "nobody" or "no one" and is used for people.

Why do we say Er zit (There sits) instead of Er is (There is)?

When describing something located inside a container, like a bag (de zak), a box, or a pocket, Dutch strongly prefers the verb zitten (to sit) over zijn (to be). So Er zit niets in de zak is the most natural way to say "There is nothing in the bag."

Why isn't there a word for "not" in the second half of the sentence?

The word niemand (nobody) is already negative. Just like in English, standard Dutch uses a single negative word to make the whole clause negative. Adding niet (not) would be a double negative, so we simply say niemand gelooft mij.

Could I say niemand gelooft me instead of mij?

Yes, you could. Both me and mij mean "me" as an object pronoun. Using mij instead of the unstressed me just adds a little extra emphasis, showing that the speaker is frustrated that nobody believes them in particular.