What is the ruling on performing dry ablution (tayammum) instead of the ritual bath due to severe cold?
Whoever is sick such that he cannot use water, or finds the water cold and heating it is not possible, and the person would be harmed by using cold water, it is permissible for him to perform tayammum. He must make up what he prayed with tayammum, because this is a place where there is water. And Allah the Almighty knows best.
What should a person do if they suffer from an incurable illness that prevents them from fasting?
A person who has an illness that is not expected to be cured and prevents them from fasting must feed a needy person one mudd (600 grams) of food (such as wheat or rice) for each missed day instead of fasting.
Allah Almighty says {what means}: "and [in such cases] it is incumbent upon those who can afford it to make sacrifice by feeding a needy person." [Al-Baqarah/184].
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.
Is it permissible for a praying person to make supplication in each Sajdah (a prostration) of obligatory prayer?
It is permissible for a praying person, whether praying individually, or in congregation, to make supplication during Sujood (prostration) in obligatory, or voluntary prayers. However, it is disliked for the Imam to do so since he is required to spare the prayer performers any sort of hardship, unless he is leading a certain group who don`t mind him extending the prayer.