Is it permissible to offer mandatory prayer while sitting?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.
Is prayer nullified by nose bleed?
All praise be to Allah, The Lord of The Worlds. Blood coming out of the nose, or a wound doesn`t nullify prayer regardless of its quantity. And Allah Knows Best.
Can someone who begins a voluntary fast break it?
It is preferable for someone who begins an act of worship not to break it.
Allah the Exalted has said {what means}: "and let not your [good] deeds come to nought!" [Muhammad/33].
However, if a person starts a voluntary fast (nafl) and needs to break it, they are going against what is preferable, but there is no sin upon them.
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.