I broke my oath and am now obligated to pay the expiation for a broken oath (kaffārat al-yamīn). Would it be valid to fulfill this by inviting the poor and needy to a meal for them to eat from?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
The expiation for a broken oath (kaffārat al-yamīn) is given to the poor (fuqarā') and needy (masākīn), and it must be given in the form of ownership (tamlīk) transferred to them of the required amount — namely, one mudd of the staple food of the locality, or its equivalent monetary value. It isn`t valid to invite the poor or needy to a meal prepared for them to eat from, as this does not constitute "ownership" (tamlīk) but merely "permission to partake" (ibāḥah).
Imam al-Shirbīnī (may Allah have mercy on him) said: "What is intended is that ownership be transferred to them; therefore, providing them with lunch or dinner [as a meal to eat from] isn`t valid." [Summarized from Mughnī al-Muhtāj,Vol. 5/P.50]. And Allah the 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.
Which is more excellent for a woman: to pray in the mosque or in her house?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Our Master the Prophet ﷺ said: 'It is more excellent for a woman to pray in her house than in her courtyard, and more excellent for her to pray in her private chamber than in her house.' Therefore, a woman’s adherence to her home and her refraining from going to the mosques—in obedience to the command of Allah the Exalted—attains a great reward and abundant recompense. Furthermore, women praying in congregation within their homes is better than their attendance at the mosques, based on the aforementioned Hadith. And Allah the Exalted knows best.
What is the ruling on preparing food for someone who is not fasting in Ramadan?
It is forbidden to prepare food for someone who is breaking their fast without a valid excuse in Ramadan.
Doing so would be assisting in sin, and assisting in sin is itself a sin.
Allah says {what means}: "but help ye not one another in sin and rancour" [Al-Mai`dah/2]