Are offering gifts to officials to facilitate work and obtain rights, accepting gifts from beneficiaries after fulfilling their needs, and using the fax and computer provided to the administration for work purposes considered permissible or forbidden?

Employees are hired laborers; it is not permissible for them to ask for an increase in their salaries. This falls under the category of forbidden gifts to workers. It is also not permissible to pay what is called a gift to employees because it is a forbidden bribe, unless they refuse to perform their duty and you find no alternative but to pay, on condition that you do not take something that is unlawful for you through this bribe.

It is forbidden for you to accept a gift in exchange for your obligatory work, and you must return it. If the giver obtained something he did not deserve because of it, then do not return it to him, and it is not permissible for you to benefit from it; rather, spend it on the general welfare of Muslims. As for the two devices, you have done what is required by putting them to use for work, and you must refrain in the future from accepting such gifts and repent to Allah.