Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?

It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.

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 for a woman to swear a false oath by the Holy Quran to please her distrustful husband?

It is forbidden for a person to do so since this is considered a false oath (Yamaan Ghamoos) which dips (Yaghmos) its taker in Hellfire if he/she doesn`t seek repentance, and he/she has to expiate for that oath. You should avoid any doubtful acts so that your husband`s chest remains clear from the evil suggestions of the devil.

I`m a cashier at a branch of the Civil Service Consumer Corporation. Sometimes, customers pay more than the due amount. Do I have the right to take that extra money knowing that I cover shortages from my own salary?