What is the meaning of a "Kafir Harbi" (belligerent disbeliever), and does its description apply to every non-Muslim who is neither a Dhimmi nor a signatory to a treaty, or is it restricted to those who have taken up arms or intended to do so?

A kafir harbi (belligerent disbeliever) is someone with whom Muslims have no treaty, no covenant of protection (aman), and no dhimma contract. The rulings concerning belligerent disbelievers apply only when jihad is lawfully permissible. For jihad to be permissible, the enemy must refuse to accept the true religion, there must be no aman or treaty between them, and the Imam must hope for strength for the people of Islam. If a Muslim enters the land of war under protection (aman) or is captured, it is not permissible for him to betray them in person or property, as that would be treachery. Jihad in Islam was legislated to ward off fitnah (strife/persecution), to invite to the truth, and so that the Word of Allah may be supreme, not for shedding blood or seizing wealth.