How should the udhiyah be distributed?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is obligatory to give the poor a portion of the meat from a voluntary sacrifice (Udhiyah al-Tatawwu’), which should not be less than approximately half a kilogram of raw meat. Other parts do not suffice for this obligation, such as the liver, tripe, or intestines.
It is Sunnah for the one offering the sacrifice to divide it into thirds: one-third for himself and his household to eat, one-third to be given as charity to the poor, and one-third to be given as a gift to friends and neighbors, even if they are wealthy. And Allah the Almighty knows best.
I bought an apartment, and I am saving money to pay the remaining balance of its price — is zakāh obligatory on this money?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Zakāh is obligatory on all saved/hoarded wealth. Once the total wealth reaches the niṣāb (minimum threshold liable for zakah— equivalent to the value of 85 grams of pure 24-karat gold) and a full ḥawl (lunar year) has elapsed over it, zakāh becomes obligatory at a rate of (2.5%) — even if the wealth is earmarked for basic future needs, and even if the wealth's owner is in debt. Debt does not prevent the obligation of zakāh, nor is it deducted when calculating the zakāh due, based on the general and unrestricted wording of all the Qur'anic verses commanding zakāh, which draw no distinction between someone in debt and anyone else.
It is stated in ‘Umdat as-Sālik, from the books of the Shāfi‘ī school: "If someone possesses exactly the niṣāb, and owes an equivalent amount in debt, zakāh remains obligatory on what is in his possession, and the debt does not prevent this obligation" — meaning, the obligation of zakāh on what is presently in his possession.
The ḥawl (annual cycle) recognized for zakāh, as well as for the other sharī‘ah obligations that Allah, the Exalted, has imposed upon Muslims, is the Hijrī (lunar) year. And Allah, the Exalted, knows best.
What is the ruling on X-ray imaging while fasting in Ramadan?
X-ray imaging itself does not break the fast. However, if a person ingests a contrast agent or medication to enhance the imaging process through an open passage to the body cavity (jauf)—such as the mouth or rectum—then their fast is invalidated.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.