Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
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.
Is a woman's prayer performed while following an Imam whose prayer is being broadcasted via the television valid, and does she receive the reward of congregational prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Among the conditions for the validity of following an Imam (Iqtida’) is that the Imam and the follower must be in the same location. Therefore, the prayer of one who follows an Imam whose prayer is being broadcasted via television from a distant location is not valid. However, if the follower is with the Imam in the same mosque, the prayer is valid. And Allah the Exalted knows best.
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.