Yes. In fact, once they "think" of the rules they want to impose on reality, they don't even need to think anymore to keep applying them. Judgements are stars, and their light impose the laws of reality anywhere they shine on, and they decide which concepts and laws of reality exist or how they work. And, yes, they can erase concepts, although it is hard to give examples of one "erasing" a concept. It's more that they allow certain concepts to exist or to not exist where their light shines, and once they do not allow it anymore, it simply ceases to be.
It is omnidirectional and influences everything the light shine on, and mere "cover" does not work well, as the light of a Judgement applies to entire planets, moons and more, it needs to be in the depths of a planet or have special shielding for a Judgement light not to reach it. The Dawn Machine however is on a weird spot, as it is a bit of a failed, if powerful, artificial Judgement, and its reach is quite small compared to other Judgements; it only covers several dozens of kilometers omnidirectionally. It might be because it is restricted by other beings in the Neath, it might be because there's some lore tidbit I've missed that limits it, it might be because it limits itself. In any case, assuming the leat, we can say that it covers very wide areas that encompasses several dozens of kilometers around it in all directions.