Does burping (belching) break the fast?
Burping does not break the fast. However, if anything comes up from the stomach, the fasting person must spit it out and rinse their mouth to cleanse it.
If they swallow it intentionally while being able to expel it, or if they swallow their saliva before rinsing their mouth, their fast is invalidated.
Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
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.
What is the ruling on a person in a state of major impurity (junub) walking or eating before performing the ritual bath?
It is from the Sunnah for a Muslim to hasten to perform the ritual bath for major impurity. However, if he delays it, he does not sin provided he does not miss the prayer. It is permissible for the junub to walk, eat, drink, and sleep. It is recommended for him to perform ablution before these actions to reduce the state of impurity, although the best is for him to perform the ritual bath. And Allah the Almighty knows best.