If I create a one-hex image of a mobile actor (an animal, a cop, a thug) can it move out of the area in which it was created? Or can it only move within that area?

An Image is able to move within the Area bought for it (if the Image doesn’t have the Area Of Effect Advantage, then it can only move within the 1m radius Area where the character created it). If the Image is bought with the Mobile (+½) modifier to Area Of Effect, then the whole Image can move according to the rules for that Advantage, which could make the characters or objects within it potentially seem to move long distances. (If the Image only affects a 1m Area, then a character can buy Mobile for it without buying the base Area Of Effect, as noted on 6E1 324.)