What is the Islamic ruling on one who was unable to fast and then regained the ability?
He is not required to make up the fast (Qada) even if he becomes capable of it; whether he regained the ability to fast after paying the fidya (feeding a needy person for each day of missed fasting) or before it, because he was liable for paying it in the first place, so it remains binding upon him. However, if he delayed paying it beyond the first year, nothing is required of him due to the delay. If he is unable to pay it, it does not remain as a debt upon him. And Allah the Exalted knows best.
Does tooth extraction during the day in Ramadan break the fast?
Simply extracting a tooth during the day in Ramadan does not break the fast. However, if water or blood enters the body cavity, the fast becomes invalid.
Whoever's fast is invalidated in this way 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 later.
It is preferable to postpone the extraction until nighttime or after Ramadan if possible.
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.
What is the ruling on eating from one`s Udhiyah?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Sacrifices (Udhiyah) are categorized into two types: the Vowed Sacrifice (Al-Mandhurah) and the Voluntary Sacrifice (Al-Tatawwu').
1. The Vowed Sacrifice (Al-Mandhurah)
The vowed sacrifice is obligatory due to the person’s specific oath. It is not permissible for the person offering the sacrifice, nor for those they are legally responsible for financially supporting (dependents), to consume any part of its meat or fat. Furthermore, it is not permissible to benefit from its hide, hair, or any other part.
If they do consume any part of it, they are required to give in charity an equivalent amount of meat or its market value [Tuhfat al-Muhtaj, by Ibn Hajar al-Haytami (9/364)].
2. The Voluntary Sacrifice (Al-Tatawwu’)
Regarding the voluntary sacrifice, it is permissible for the one offering it to eat from its meat, distribute it as gifts to the wealthy, and give it as charity to the poor.
The Obligatory Portion: It is mandatory to give at least a small portion of it in charity to the poor; this portion should not be less than approximately half a kilogram of raw meat. And Allah the Almighty knows best.