Yes, that's all pretty correct. Of course there's a lot of detail that's glossed over here. For example, how many "hops" away I want to replicate is a parameter. My client can request any feed from any peer that it connects to and hope they have it. So nothing is stopping me from putting "hops": 7 into my ~/.ssb/config and start replicating effectively the entirety of what my client can reach.

how recent?

That really depends on how fast people move & mix. So these days... faster in NZ, slower in the US & Europe. 😐
I'm sure there's interesting networks research around how fast information will spread, and it is probably actually relevant to the epidemiology experiment we're all living through right now. But I'm not aware of it. I just assume that messages spread "slowly" when there's no pubs.