What is the ruling on ablution without istinja' after sleep?
The sleep of one whose buttocks are not firmly seated on the ground invalidates ablution. Whoever wakes up and wants to pray must perform ablution only. Istinja' is not a condition for the validity of ablution, because it is for removing impurity from the private part. If there is no impurity on the private part, then istinja' is neither obligatory nor recommended. And Allah the Almighty knows best.
Is it permissible for one to give the Zakah (obligatory charity) to his indebted brother?
It is permissible for one to give the Zakah to his brother if he was indebted, or poor.
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.