Learn Italian: Voleva dormire, ma ha dovuto studiare. - She wanted to sleep, but she had to study.

This perfectly shows how these tenses change the meaning of modal verbs! Voleva describes an ongoing state of mind in the past: she simply had the desire to sleep. Ha dovuto, however, describes a completed, specific event. The obligation forced an action that was actually carried out.

Does ha dovuto studiare guarantee that she actually studied?

Yes! In Italian, using the passato prossimo with a modal verb means the action was definitively completed. She had to study, and she actually did it. If the sentence used the imperfetto instead (doveva studiare), it would mean she was supposed to study, but it would leave it open as to whether she actually did or not.

Why is the auxiliary verb avere used in ha dovuto instead of essere?

When a modal verb is followed by an infinitive, it usually borrows the auxiliary verb that the infinitive requires. Because you use avere with studiare (for example, ha studiato), the modal also takes avere here. If the infinitive took essere, like andare, the modal would typically take essere too (è dovuta andare).

The translation says She wanted, but could voleva and ha dovuto also mean He wanted and he had to?