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.
What advice do you have for those who spend their nights and days of Ramadan watching TV?
Time is too precious to be wasted on entertainment, let alone in the blessed month of Ramadan, where a Muslim should strive for reward and forgiveness.
Should a prayer performer who forgets to offer the middle Tashahod (saying ash-hadu anala ilaha ila-alah) offer Sujood As-Sahw (prostration of forgetfulness)?
He/she should offer two prostrations of forgetfulness at the end of the prayer. And Allah Knows Best.
Does vomiting during the day in Ramadan break the fast?
Intentional vomiting is one of the nullifiers of fasting; whoever vomits deliberately breaks their fast.
However, if vomiting occurs involuntarily, the fast remains valid as long as nothing returns to the body cavity (jauf). If anything is swallowed back, the fast is invalidated.
The Prophet ﷺ said: "Whoever is overcome by vomiting does not have to make up the fast, but whoever induces vomiting deliberately must make it up." [Narrated by Abu Dawood and At-Tirmidhi]