Earth had Saturn-like rings 466 million years ago, new study suggests

466 million years is recent. And short. Could such structure exist with the tide of the moon? Was the tide any stronger at that time? Was the moon always locked?

I’m guessing to be wrecked up and out there, the rock would have to be soft, or a sand pile. Not much to reach the surface. No large impacts.

There might be other factors and reasons for the locations of the studied impacts.

It might take 466 million years just to establish a ring.

Are rings caught and aligned, or are rings spewed out?
 
Could such structure exist with the tide of the moon? Was the tide any stronger at that time?
The Earth-Moon Roche limit, according to NASA, is about 19,900 km
Even at the closest point in its orbit, the Moon is 363,104 km [out]
https://www.skyatnightmagazine.com/space-science/roche-limit

So the Moon is 20 times further out. Even Saturn have long term rings despite large moons et cetera, but these became just 30 million years old (see the paper). The rest of your questions should be covered by the paper's model.
 
Why does it have to have been a "ring" of tiny particles? They don't leave impact craters, anyway. Another scenario would be that an asteroid broke into pieces when it came within the Roche limit, but those pieces orbited multiple times before individually impacting Earth. Jupiter did that to a comet not long ago.

The "ice age" may or may not be related. If there was enough ejecta from the impacts, would we have had cooling effects from dust thrown into the atmosphere by the impacts? Could that have been a "tipping point" in Earth's climate balance, rather than a sustained cooling by the dust?

Finding a lot of craters 400,000,000 million years old suggests to me that they must have been substantial impacts to have produced evidence that survived Earth's weathering processes for that length of time. And, those are just the ones that hit the continents - how many hit the oceans?

For that matter, why would it have to be an "asteroid"? Why not a second, smaller moon that was created at the same time as the Moon we all know, love, and want to get back to? Maybe that second moon's orbit slowly lowered while the Moon of today's orbit slowly rose, as is currently happening with the 2 moons of Mars? When the smaller, lower moon finally got within the Roche limit, it broke apart and eventually led to multiple impacts, maybe with a ring.

Just because a theory might fit the sparse data does not make it a sure thing.