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Fun story: One of the Grand Finale measurements was the mass of the rings (dominated by the B ring). I wrote a prediction paper that it would be more massive than most thought, based on simulations of clumping and how you can effectively hide mass in the B ring. Unfortunately, the Grand Finale measurements proved my paper wrong. Okay, maybe not-so-fun story.
Welcome to the site. I'm not really sure if your question has an answer, given that we don't fully understand core dynamos. Your question is also a bit vague in that you seem to be allowing "other minimum properties" beyond size. A stable magnetic field can also be formed without a core dynamo, so for example there's speculation that Pluto might have a magnetic field due to convective liquids. You also don't really need a dynamo for life, though it certainly helps to protect from charged particle radiation (but so would an ocean, or being underground). I'm interested in any answers though.
Pretty sure you wouldn't, but it all depends on composition and energy. Stuff in the Kuiper Belt has <2 km/sec impact speeds, which is 10x smaller than at the Moon. Stuff in the Kuiper Belt is icy, not rocky, so impacts work differently, as do their accompanying flashes. We haven't see any impact flashes anywhere on any other bodies other than the Moon, so whether one would expect to see it on a hypothetical body that is literally >1000x farther away is pretty much a "no" to me, even if the flash in ice were as bright and even if it had the energy of an inner solar system impactor.
There are definitely similar clouds on Mars, I've seen them in Elysium in some MARCI images I've processed. But, I suspect you would need to go to Viking to get the AMEC images simply because NASA orbiters since the late 1990s have focused on afternoon imaging of the surface, so you'd never see the AMEC with them. Hence, MEx and MOM are the ones to really provide modern data on this.
And, I also can't find it on the map of the Moon, so now I'm confused. It's not Venus, it's not Mars. We don't have topography that good that looks like that for the Galilean satellites, and I'm pretty sure the Saturnian are much more heavily cratered and don't have large craters with almost nothing emplaced on them. I know it's not Pluto/Charon, I helped make those maps. Vesta does not have any craters like that, so I suppose Ceres is a possibility. It's also possible I simply missed it on Mercury. There're named craters on the map (white horizontal rectangles, but much too low-res to read.
It is a topographic (rainbow colorscale) digital terrain model of some body. I'm 90% sure it's Mercury and not the moon. However, I've never really tried hard to figure out where it is. I think it's Mercury because of the piecemeal nature of the data: On the Moon, we have very good topography with no gaps, but on Mercury the topography made from stereogrammetry from framing camera images, and there were plenty of gaps in the data when I think that image first appeared on their refrigerator.
Not my field so I'm just making a comment: (a) Cannot be detected from Earth because they are too small, you must have an orbiter camera. (b) Other comments noted a list, though I don't know of any one that is actively maintained. (c) It only requires images with enough resolution to see the pits, you don't need laser nor radar. (d) Radar has a HUGE footprint for a given "pixel," so while I suspect radar could be used in theory, it is not useful in practice.