Is it permissible for a woman whose menses exceeded (15) days to pray, fast and do what was prohibited on her to do during the latter period?
If the menses exceeded 15 days then it is deemed menstruation, and in this case she is obliged to pray and fast and to do what was impermissible for her to do during the latter period. In addition, she is obliged to make an ablution for each obligatory prayer after it's due time and making sure that impuity is removed. Finally, your menstruation period is over (Questioner) simlar to your menstruation in the previos month.
Is it permissible for the guardian, or the father of the child to hit the latter in order to teach him/her good manners?
It is permissible for the guardian to hit his/her child for teaching them good manners once they become ten years old provided that it is done mildly, harmlessly and without intimidation. Actually, such punishment is to be employed gradually i.e. after: asking, warning, and scolding. As for the teacher, he isn`t allowed to hit the student unless the latter`s father approves of it, and it is done according to necessity without intimidation, or harm.
If the fasting of nine years has accumulated upon me, I wish to make them up by dividing them over several years, as it is difficult to fast them all in one year due to their large number. Consequently, expiation will be due on me. Is it permissible to pay the expiation after completing all the make-up fasts, even if it takes years?
If the fasting was broken due to a valid legal excuse, it is permissible to divide the make-up fasts over several years based on one’s ability. However, if a person passes away before completing the make-up fasts, the heirs must fast on their behalf or feed one needy person for each missed day.
If the fasting was broken without a valid excuse, one must hasten to make it up. Should the person die before completing the make-up fasts, the heirs must either fast or feed the needy on their behalf. As for the expiation, it is calculated after completing all the make-up fasts. And Allah Knows Best.
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.