Is it permissible to read from the Mus-haf during Tarawih prayer?
Yes, it is permissible to read from the Mus-haf during Tarawih prayer, provided that excessive movements that invalidate the prayer are avoided.
However, it is preferable for the imam to be a memorizer of the Quran and to recite from memory.
If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?
It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.
What is the ruling on seeking forgiveness between the two Friday sermons?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible to seek forgiveness (Istighfar) between the two Friday sermons (Khutbatayn), and it does not invalidate the Friday prayer (Salat al-Jumu'ah). Furthermore, it is not disliked (Makruh) to speak before the sermon, after it, or between the two sermons. Likewise, it is not disliked for one who enters during the sermon to speak if there is a need for it, provided he has not yet taken a place and settled into it. And Allah the Exalted knows best.
Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded. And Allah Almighty knows best.