What is the ruling on paying a sum of money to Saudi citizen in return of having Saudi residence? It is worth noting that this transation is labelled as a "worker's visa" but I am not going to work as such only to facilitate having it?

Is it permissible to offer mandatory prayer while sitting?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.                                                                                                                                                                                                                            Standing up is a pillar in the mandatory prayer and the prayer is not valid without it unless one cannot do it. As for Nafila (supererogatory prayer), one can perform it in the state of sitting even if he/she can stand, but his/her reward is half the reward of the person who prays while standing if he/sh has no legal excuse for such an act. And Allah Knows Best.

Zakah due on a woman`s jewelry?

Obligatory Zakah (obligatory charity) isn`t due on a woman`s jewelry used for adornment, provided that the value of each piece is within the range amongst common market price. And Allah Knows Best.

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.