Does nosebleed during the day in Ramadan affect the validity of fasting?
A nosebleed does not affect the validity of fasting unless some of the blood reaches the body cavity or the person intentionally swallows it. In such a case, their fast is invalid, and they must refrain from eating and drinking for the rest of the day and make up for that day later.
Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
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.
I own a pharmacy and have only merchandise. A full year (*ḥawl*) has passed and I have no cash. How do I pay the zakāh?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Zakāh must be paid immediately from the day it becomes due, and delaying it is forbidden when one is able to pay it, because it is the right of the poor, and it is forbidden to delay giving people their rights except for a valid Sharīʿah excuse. Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him) said: “In our school, zakāh must be paid out immediately. Once it becomes due and he is able to pay it, it is not permissible to delay it. If he is unable, he may delay it until he is able. If he delays it after being able, he is disobedient and becomes liable for it.” [al-Majmūʿ Sharḥ al-Muhadhdhab, Vol.5/p.333]
If cash is not available to pay the zakāh and the only option is to pay in installments, he must pay it, even if in installments, from the proceeds of the merchandise that is sold after the time the zakāh became due, by deducting a set amount from each day’s takings. And Allah Almighty knows best.