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].
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.
Is it permissible to say: "O Allah, by the status of the saints and the righteous, and our master Muhammad, peace be upon him, grant us the ability to reach Ramadan"?
What is mentiond by the righteous predecessors that they used to say: "O Allah bless us in Shaba'an and Rajab and give us the ability to reach Ramadan." [Shoa'ab Al-Iman/vol.3/pp.375]. And Allah Knows Best.
Is Zakah due on the orphan`s money?
Yes, Zakah is due on the money of the orphan.