Something I'm contemplating: If one faction destroys a large structure of an enemy faction with a nuclear device equivalent to a WWII atomic bomb on the moon. Would the force of the explosion be enough to push the moon off its orbit to some extent?
No, the force of an Atomic blast isn't enough to significantly alter the Moon's orbit. Even the combined force of humanity's current nuclear stockpile is only enough to offset it the Moon's orbit by an unimaginably small amount.
Here's an answer to a similar question if you want more information:
It wouldn't. A lot of people seem to think nukes are cosmically powerful, likely because of how devastating they are to our structures. But compared to a celestial body it's nothing, you'd need a substantial volume of antimatter explosives to destabilise such a large body, and even then doing so would simply rupture the moon into pieces.