Learn Italian: Nessuno è rimasto sveglio fino all'alba.

The compound preposition fino a means "until" or "up to". Because the noun alba (dawn) requires the definite article l', the preposition a combines with it to form the articulated preposition all'.

I thought Italian used double negatives. Why is there no non before the verb here?

In Italian, when a negative pronoun like nessuno (nobody) is placed before the verb, you drop the non. You only use the double negative if the verb comes first, which would look like this: Non è rimasto sveglio nessuno.

Why is the auxiliary verb è used with rimasto rather than ha?

The verb rimanere (to remain/stay) is a verb of state. In Italian, verbs describing state, motion, or change of state take essere (to be) as their helping verb in compound tenses like the passato prossimo.

If we were talking about a group of women, would it change to Nessuna è rimasta sveglia?

No, it stays exactly the same. As a pronoun meaning "nobody", nessuno is always grammatically masculine singular. Therefore, the past participle (rimasto) and the adjective (sveglio) must agree with it and remain masculine singular, regardless of the actual gender of the people involved.