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.
Is prayer mandatory on a dying person who goes through a state of unconsciousness, then wakes up?
If he wakes up and was conscious, then he should pray the way/manner he could, but if he wasn't, then he is exempted from obligatory prayer as Allah Says in this regard (What means): "On no soul doth God Place a burden greater than it can bear." [Al-Baqarah/286].
Is it permissible for a Muslim woman to uncover her hair in the presence of a Christian woman?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
According to the reliable opinion of the Shafie School of Thought, this isn`t permissible. However, some scholars stated that it is permissible for a woman to uncover what she usually uncovers while doing housework, but this differs from one place to another where some women uncover their hair while some don`t. However, this is provided that a woman doesn`t uncover her hair in the presence of non-Mahram men (Men permissible for a woman to marry). And Allah The Almighty Knows Best.
What is the ruling on Friday Ghusl (ritual bath)?
Friday Ghusl is a confirmed Sunna (Prophetic tradition) even if a person wasn`t in a state of Janbah (ritual impurity), or physically unclean. However, one who doesn`t make Ghusl on Friday isn`t sinful for the Prophet (PBUH) said: "It is good for a Muslim to make ablution for Friday prayer, but it is better to make Ghusul. [At-Tirmithi & Abu Dawood].