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, but not an udhiyah. And Allah Almighty knows best.
Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
Is it correct that everything dry is pure even if it has impurity on it?
If something impure becomes dry, it remains impure and is not purified by drying. However, the impurity does not transfer by touching it if the one touching it is also dry. And Allah the Almighty knows best.
If a woman becomes pure from menstruation shortly after Fajr in Ramadan, what is required of her?
If a woman becomes pure (from menstrual period) after Fajr, even shortly after, it is recommended (but not obligatory) for her to refrain from eating and drinking for the rest of the day. However, she must make up for that day after Ramadan.
She will be rewarded for both refraining from eating (imsak) and making up the fast (qada) since she was menstruating for part of the day.