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.
What is the wisdom behind the legislation of fasting?
Fasting is a divine school from which the believer learns much and trains in virtues that may be needed in life. Among these virtues is patience, as it is the month of patience. Fasting also teaches honesty and consciousness of Allah in both private and public, for there is no observer over the fasting person in abstaining from lawful pleasures except Allah alone.
Fasting strengthens willpower, sharpens determination, and nurtures mercy and compassion among the servants of Allah. It is a struggle against the self, a restraint of desires, a purification of the soul, and a cultivation of goodness.
The Prophetﷺ said: "Allah, the Almighty, said: ‘Every deed of the son of Adam is for him, except for fasting; it is for Me, and I shall reward for it. Fasting is a shield. So when one of you is fasting on a day, let him not engage in obscene speech or raise his voice in anger. If someone insults him or fights him, let him say: I am a fasting person. By Him in whose hand is the soul of Muhammad, the breath of the fasting person is more pleasant to Allah than the fragrance of musk.’" [Bukhari and Muslim]
Does undergoing an endoscopy during the day in Ramadan affect the validity of fasting?
Undergoing an endoscopic procedure during the day in Ramadan—whether through the mouth, nose, front private part, or back private part—invalidates the fast.
Whoever undergoes such a procedure must refrain from eating and drinking for the rest of the day out of respect for the sacred month and make up for that day after Ramadan.
Is it permissible to offer prayer at home, or should it be offered in the mosque?
All perfect praise be to Allah, The Lord of The Worlds. It isn`t preferable for the man to pray at home as praying in the mosque is twenty seven times more rewarding. Therefore, this should motivate him to offer prayers in the mosque. And Allah Knows Best.