What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.
What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.
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.
Who is the one deemed "able" (al-qādir), for whom the uḍḥiyah (sacrificial offering) is sunnah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The one who is deemed "able" (al-qādir) [to perform the uḍḥiyah, i.e., the sacrifice] is someone who possesses wealth sufficient to acquire the sacrificial animal, over and above what is needed to cover his own living expenses and the living expenses of his wife and children — or of anyone else whose financial support (nafaqah) is legally obligatory upon him — for the day of ‘Eid and the three days of Tashrīq [that follow it], since this is the designated time period for the sacrifice. And Allah, the Exalted, knows best.