I used only probes to test this.

My probes were able to fully scan all planets in a system when they were located at that systems sun. I was able to see harvesting routes, orbitals, and planetary information. I also had the options pop up to attack and to message that player. The attack option seems strange. I ussed an attack order and it told me I was attacking, but nothing appeared to happen. The probe is alive and at the sun. I am not sure if this affected my diplomatic standing.

I have not encountered a planet near me that has a standing group of ships (or a fleet), so I can't determine if I would be able to view their details. However, I did encounter a planet that had a trade ship in orbit around the planet for a player other than the one owning the planet. I was able to view that ships details from the sun.

I happen to have a colony (not an outpost) in a system that someone else now mostly controls. Again, I am able to see all of these same things for this other persons planet in that system, including the option to attack (it does nothing again).

When I moved my probes out of the system, I was still able to see all of this information as if the probe was still there. I have since logged out and the back in, and now it is back to the default, where I cannot see any information on the planets in that system. So it looks like there is some latent information as long as I remain logged in.