How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?
Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.
Is Zakah due on the orphan`s money?
Yes, Zakah is due on the money of the orphan.
I am an author, and I have books stored with me. Is it permissible to pay my zakat in the form of books containing beneficial knowledge for poor students, such as chemistry and mathematics, or religious books that spread Islamic sciences?
Zakat on wealth must be paid in cash from the wealth itself. Therefore, you should pay your zakat in monetary form so that the poor can purchase what they need. And Allah Knows Best.
What is the ruling on someone who perform their prayer after finishing it because they believe they missed a Rak'a, a prostration, or that they did not perform it correctly (thinking their prayer was invalid)?
If he was sure that his prayer is void then reperforming it is an obligation along with figuring out the reason of invalidity so long as this wasn't out of uncertainty. And Allah Knows Best.