Is it recommended (mustaḥabb) for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from its meat?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is recommended (mustaḥabb) — not obligatory — for the one offering a voluntary sacrifice (uḍḥiyyat taṭawwuʿ) to eat from it. Allah Almighty says {what means}: "So eat from them and feed the desperate (qāniʿ) and the beggar (muʿtarr). Thus We have subjected them to you that you may be grateful."— [Sūrat al-Ḥajj (22): 36]
Explanation of terms:
Al-Qāniʿ — the poor person who does not ask people for money, food..eccetera.(beg)
Al-Muʿtarr — the poor person who does ask people for money, food..eccetera (begs)
And Allah Almighty knows best.
Can a person required to give kaffarah feed it to their own family members?
The kaffarah must be given to the poor and needy who are not financially dependent on the one giving the kaffarah.
If a person feeds it to their own family members, it does not count as kaffarah, and their obligation remains unfulfilled.
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.
Should the Zakah (obligatory charity) giver tell the poor recipient that this is the Zakah of his money?
No, he shouldn`t. But, the Zakah giver should make an intention in his heart that it is the Zakah of his money when paying it to the poor. And Allah Knows Best.