Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
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.
What are the key differences between the 'aqīqah and the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The following are the key differences between the 'aqīqah and the uḍḥiyyah:
First: The 'aqīqah is slaughtered as an act of drawing closer to Allah the Almighty and expressing gratitude for the blessing of a newborn child. The uḍḥiyyah, on the other hand, is slaughtered as an act of drawing closer to Allah and expressing gratitude to Him specifically during the days of slaughter (ayyām al-naḥr).
Second: The 'aqīqah is performed on the seventh day from the birth of the newborn, whereas the uḍḥiyyah is performed on Eid al-Aḍḥā and its time extends for three days after the Eid.
Third: The 'aqīqah is performed once in a lifetime for the newborn, whereas the uḍḥiyyah is recommended every year.
Fourth: It is Sunnah for the one intending to offer the uḍḥiyyah to refrain from cutting his hair and nails until after he has slaughtered. This is not a Sunnah for the one intending to perform the 'aqīqah.
Fifth: It is Sunnah for the 'aqīqah to be cooked and distributed to the poor in its cooked form. The uḍḥiyyah, by contrast, must be distributed as raw meat. And Allah Almighty knows best.
What is the ruling on one who performs ablution or the ritual bath while having nail polish?
Nail polish must be removed before ablution or ritual bath so that water reaches what is beneath it, because it is a barrier that prevents water from reaching that area. This is based on the hadith narrated by Ali (may Allah be pleased with him) from the Prophet (peace be upon him): "Whoever leaves a hair's breadth of his body unwashed from major impurity, such and such will be done to him in the Fire." (Reported by al-Bukhari). And Allah the Almighty knows best.