Can a woman perform I‘tikaf in her home?
No, a woman's I‘tikaf is not valid if performed at home, because her home is not a mosque.
What is the ruling on the intention of fasting, where is its place, and when is its time?
The intention is a pillar of acts of worship; it is essential, and worship is not valid without it.
Its place is in the heart, and verbalizing it is recommended so that the tongue reminds the heart. Its meaning is to be determined to abstain from nullifiers of fasting during the upcoming day with the intention of worship and obedience to Allah Almighty. This meaning is naturally present in every Muslim on every night of Ramadan, so there is no need for obsessive doubts. If one says, "I intend to fast tomorrow for the sake of Allah," it removes any doubts.
Its time is from after sunset until before the true dawn.
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.
What is the ruling of Islamic Law on compensating the patient in case of medical error on the part of the treating physician?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
The foundational principle is that every mistake issued by a physician that causes harm to another due to his negligence or lack of expertise obligates him to guarantee liability and compensate the harmed party. The Sharia maxim, in this regard, states: "The direct actor is liable."
Ibn Qudamah (may Allah have mercy on him) says: "As for if he was skilled but his hand committed an error—such as exceeding the proper limit of incision, cutting in an incorrect site, cutting with an instrument that inflicts excessive pain, or cutting at an unsuitable time—he is liable, because it is destruction (Itlaf) whose liability does not differ between intent and mistake, thus resembling the destruction of property; and because it is a prohibited act, so he guarantees liability for its secondary effects." [Al-Mughni].
However, if the physician performed what was necessary in the most complete manner and took all measures of care and caution, but complications occurred that could not be avoided according to specialists, then no liability rests upon him.
Shaykh al-Islam Imam al-Nawawi (may Allah have mercy on him) says: "The cupper and the circumciser bear no liability if they have not been negligent, and likewise the veterinarian if he bleeds an animal and it perishes." [Rawdat al-Talibin].
Al-Khattabi (may Allah have mercy on him) said: "I know of no disagreement that if the practitioner transgresses and the patient perishes, he is liable. Anyone who undertakes knowledge or practice he does not know is a transgressor; so if perishing arises from his action, he is liable for the blood-money (Diyah) while capital retaliation (Qisas) is dropped from him, because he did not act independently without the patient's permission. And the physician’s offense in the view of the generality of jurists is borne by his agnates ('Aqilah*)."* [Ma'alim al-Sunan].
If negligence or transgression is established against the physician, it is necessary to compensate the patient or seek forgiveness from him. And Allah Almighty knows best.