Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
What is the ruling on the Friday bath (ghusl al-Jumu'ah)?
The Friday bath is a confirmed Sunnah, based on the Prophet's (peace be upon him) saying: "Whoever performs ablution on Friday, it is good for him, and whoever takes a bath, bathing is better." (Reported by Abu Dawud and al-Tirmidhi who said it is a hasan hadith). It is recommended for everyone who wants to attend the Friday prayer, even if they are not from its usual attendees, like a woman or a boy.
If a person is in a state of major impurity (junub) and intends by his bath both lifting the major impurity and the Friday bath, he achieves both. If he intends only one of them, he achieves only what he intended. And Allah the Almighty knows best.
Is it permissible to give to the poor from among the People of the Book from the Udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to give to the poor among the People of the Book from a voluntary sacrifice (uḍḥiyyat taṭawwuʿ), just as it is permissible to give charity (ṣadaqah) to them. This opinion is a view (wajh) within the Shāfiʿī school, which was favored by al-Muḥibb al-Ṭabarī and Imam al-Nawawī. [See: Ḥāshiyat Ibn Qāsim al-ʿAbbādī ʿalā Tuḥfat al-Muḥtāj (Vol.9/P.365)]. And Allah Almighty knows best.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.