Learn Russian: Они верят в приметы и ожидают чуда. - They believe in omens and expect a miracle.

This is the special rule for verbs of expectation, such as ожидать (to expect) and ждать (to wait). When you expect or wait for something abstract, intangible, or indefinite—like a miracle (чудо)—these verbs require the Genitive case. Therefore, the neuter noun чудо changes to чуда.

Why do we say верят в приметы (Accusative) instead of just using the Dative case?

It depends on what is being believed. When верить means "to trust or believe a person," it takes the Dative case with no preposition (for example, Они верят мне - They believe me). However, when it means "to believe in an idea, concept, or phenomenon" (like omens, God, or magic), you must use в + Accusative case.

Is приметы in the Nominative or Accusative plural here?

It is in the Accusative plural. The singular is the feminine noun примета (omen/sign). Because omens are inanimate, the Accusative plural form looks exactly identical to the Nominative plural form (приметы).

Could I use ждут instead of ожидают in this sentence?

Yes, you could say ждут чуда, and the meaning would be exactly the same. Ожидать is simply a slightly more formal version of ждать. It is heavily used when talking about abstract expectations like a miracle, a result, or a change, making it a perfect stylistic fit for this sentence.