Is it permissible to continue receiving a military salary without working, for the purpose of seeking another job, knowing that military work is unsuitable and undesired? And is the salary received by the deceased father, the brother, and the uncle without working considered unlawful? And is the father sinful for registering them?

It is not permissible for a Muslim to take the money of others, whether an individual or a state, except through a legitimate means. A contracted employee is not permitted to breach their agreement unless authorized by the manager in a way that allows it. Your registration as a seconded employee, or your father's registration of your brother and uncle, is a deception and an unlawful consumption of state funds, which is forbidden by Islamic law. Allah (SWT) says: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know [the consequence]." (Quran 8:27) And He (SWT) says: "And do not consume one another's wealth unjustly." (Quran 2:188) Therefore, it is not permissible for you to remain in these positions unless you perform the tasks assigned to you; otherwise, it is deceit, forgery, and the consumption of illicit money. In the event that taking the money is not permissible, the money taken must be returned to the state treasury if those in charge of it are just in its distribution, based on the Prophet's (PBUH) saying: "On the hand is what it took until it returns it." Otherwise, it should be spent on general Muslim interests or given as charity to the poor.