Is performing Umrah an obligation for who is capable. Is he accountable for not performing it in this case?
Umrah is an obligation once in a lifetime for every Muslim. When physical and financial ability is present, it is preferable to perform Umrah, as well as Hajj. If one can afford to perform Umrah but not Hajj, then they should begin with Umrah, especially since Hajj nowadays is not accessible to everyone who wishes to perform it. In contrast, Umrah is more open and easier to undertake. And Allah knows best.
What should a worshiper who has forgotten a pillar of prayer do?
If he/she remembered the forgotten pillar before offering it in the following Rakah (unit of prayer), then he/she should offer it, and continue the prayer, then offer Sujood As-Sahw (Prostration of forgetfulness) at the end of it. But, if he/she remembered that forgotten pillar after having offered it in the following Rakah, then he/she should offer a new Rakah in its (the one in which he forgot a pillar) place, and offer Sujood As-Sahw.
Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.
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.