Is it valid to perform Tarawih prayer at home?
It is Sunnah for a Muslim to perform Tarawih prayer in congregation at the mosque.
However, if a person sometimes prays it at home in congregation with their family for a valid reason, there is no harm in doing so.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Do wounds and bleeding during the day in Ramadan break the fast?
If a wound results in something entering the body cavity (jauf), such as blood or an external object, then the fast is invalidated.
However, external wounds and bleeding do not break the fast, unless they cause something to enter the body cavity.
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.