PTW, and I have numerous ideas:
* If at all possible, try to have the moon believe that we don't mean any harm. Maybe send down an unarmed drone which can transmit messages. Maybe we can send a copy of a blueprint (ofc not a dangerous one, maybe a miner) as a token of goodwill. If we can get them to side with us, we might be able to learn more about the situation.
* I do believe that we could eventually get an asteroid base, but I rather believe that we should move operations to it, while keeping us in an easily identifiable (as being artificial) shell. The reason being is that if the asteroid falls from orbit, the size it has would make escaping orbit again difficult if not impossible, while also making neutral parties believe it is a natural asteroid, which could destroy us.
* Since we don't know a whole lot about our purpose, we should try to be on good terms with _everyone_ until we know the purpose. Then, in the offchance we are supposed to destroy someone, we can both evaluate the instruction to see if that is actually the best thing to do, and if it is, they won't know what hit them since we are supposibly on their side.
* I support the drone ship idea, but I believe that it should have the capabilities of eventually housing us. If the moon turns out to be 100% hostile, we shouldn't hang around, and a falling-apart satallite-ship-space-station-thing is not the best thing to move around in, especially since the only thrusters are only suitable for maintaining orbit.
* Are the asteroids we see what the presumed destroyed planet became? If so, send at least one eye down to investigate the remains. Maybe also design a modified eye which has probing capabilities, like the Mars rovers? It might be better to prospect asteroids before mining them, since we might just end up using up materials to find that an asteroid has nothing of value in it or, worse yet, some other AI (another reason to not move to an asteroid)
EDIT: Since we in our form right now are rather vulnerable, the drone should report that we are a hivemind AI composed of the drones. If the moon gets angry, they will hopefully target all the drones; if this happens, we can design some dummy drones which don't have any useful functunality and send out a swarm of them to distract the moon. If the moon trusts us from our goodwill, then when we eventually move to a more secure shell, we can report that we weren't actually a hivemind, but we reported that for our own safety, since said moon had an aggressive response in the past, and that we were actually were in the sattelite the drones came from. Ofc we had already moved out of there, in case the moon gets angry. But telling the truth might help build the trust a bit more
EDIT: WAIT A SECOND!!!
What if _we_ nuked the planet, and the EMP from the nuke knocked us out, as well as all the files less some specific ones? Or the ones that were wiped were never there in the first place?
That is only speculation, mind you, and there is just about zero proof for it.