Not necessary, because even if they weren’t the dominant form of artistic expression, the existence of paintings/engravings representing warfare can still indicate the presence or absence of war.

Not necessary, because the reasoning isn’t based on any belief about the specific reasons for war. Although the author does believe a transition to agricultural societies caused warfare to develop, he doesn’t say anything that suggests a belief about what exactly those warring societies fought about.

Necessary, because if it were not true — if there WAS warfare prior to the period in which paintings/engravings of warfare were first created — then we cannot be sure that there was no warfare before the period in which agriculture first developed. There might have been warfare even before agricultural societies came about. The author must assume this isn’t the case in order to conclude that warfare “first” developed from the transition to agricultural societies.

Not necessary, because the author doesn’t have to have any belief about what is “inevitable.” The author does argue that a particular historical transition caused warfare, but that doesn’t mean the author thinks that in an alternate timeline, the transition to an agricultural society was guaranteed to cause warfare. (I can say that my fall yesterday caused me to break my leg without believing that it was inevitable that the fall would break my leg.)

Not necessary, because the argument concerns the presence or absence of paintings/engravings representing warfare. The author never relies on any claim about paintings/engravings that represent anything else besides warfare, such as representations of agricultural life.