What is the ruling on someone who prays but does not fast, without a valid excuse?
Fasting is one of the pillars of Islam, and a Muslim's faith is incomplete if they neglect the obligation of fasting while being physically capable of observing it.
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.
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.
What is the ruling on a person in a state of major impurity (junub) or a menstruating woman (ha'id) reciting the Quran from memory?
It is not permissible for a menstruating woman, a postpartum woman, or a person in a state of major impurity to recite anything from the Quran, whether from memory, from the Quran, from a phone, or a computer. It is also not permissible for them to touch the Quran, based on what was reported from Ali bin Abi Talib that the Prophet (peace be upon him) was not prevented from anything regarding the Quran except major impurity (janabah). (Reported by al-Tirmidhi who said it is a hasan sahih hadith). Menstruation and postpartum bleeding are analogous to major impurity (janabah) as they are all major impurities (hadath akbar).
For those mentioned, it is permissible to mention Allah and supplicate even with verses from the Quran, provided they do not intend them as recitation of the Quran, but intend them as remembrance (dhikr) or supplication (du'a). And Allah the Almighty knows best.