Is it permissible for a woman to read the Qur’an from the Mus'haf (physical copy of the Qur'an) during Tarawih prayer, and is it obligatory for her to perform the entire Tarawih prayer (20 rak'ahs) in the first third of the night immediately after the 'Isha' prayer?

It is permissible for someone who has not memorized (the Quran) to read from the Mus'haf (Quranic text) during prayer. Tarawih prayer is a confirmed Sunnah, not obligatory, and it is not required to be performed consecutively. Therefore, it is permissible to perform it in its entirety or divide it over the hours of the night, with a preference for performing it in the last third of the night.