What is the punishment for a Muslim who kills a Dhimmi (a non-Muslim living under Muslim rule), and is he to be killed for it, and if so, what is the punishment that is carried out against him?

A dhimmi is someone with whom Muslims have an agreement and covenant. They must be protected, and it is forbidden to aggress against them. A Muslim who kills a dhimmi is threatened with a severe warning. A Muslim is not killed for a disbeliever, whether the disbeliever is a dhimmi, a mu'ahid (one with a treaty), or a musta'min (one granted safe conduct). As for the punishment of one who kills a dhimmi: if the killing was accidental, the blood money (diyya) is half that of a Muslim; if it was intentional, the blood money is made severe, like the blood money of a Muslim.