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.
What is the ruling on undoing braids of hair during the ritual bath?
It is not a condition to undo braids if the water reaches all the hair and penetrates to its base. If the water does not reach except by undoing the braids, then it is obligatory to undo them for the water to reach. And Allah the Almighty knows best.
Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
Is fasting obligatory for a child?
Fasting is not obligatory for a child until they reach puberty. Puberty is determined by well-known signs, the most common of which are: nocturnal emission (for both males and females), menstruation (for females), or reaching the age of fifteen lunar years.
A guardian must instruct their children to fast once they reach the age of discernment, which is around seven years old, if they are capable of fasting.