Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded, but not an udhiyah. And Allah Almighty knows best.
What is the ruling on a young man and a young woman having a love relation for the purpose of getting married?
It is forbidden for a man and a woman to have any kind of relation whether for marriage, or not because it leads to committing sin. Such relations include: private meetings, mixing, gazing, and seclusion (Khulwa). Accordingly, one who is sincere in his intentions should go to the woman`s guardian and ask for her hand in marriage.
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.