Sorry, I'll try and be more specific:
(1) You and I were flying together, in our own ships, chasing the same enemy, that enemy being CMDR Codger, (importantly, not an NPC).
I log out of ED, leaving you on your own chasing CMDR Codger and you destroy him.
Hence, would he be there when I log in to ED again as I would expect him to be ?
Or would you have to advise me you'd defeated him?
Remember he's not an NPC.
(2) If CMDR Codger want's to escape, away from both of us, I assume he can't simply just log out.
This I assume is because his craft, piloted by God knows who, will still be flying in ED, trying to evade you and me.
Is this the case ?
I assume these scenarios are only possible in OPEN Play, which I'm extremely unfamiliar with.
Therefore what I describe above, might be a load of impossible nonsense .....
What Codger wrote is correct.
After a player is destroyed, they rebuy their ship and then they are back and they are the same CMDR. They are persistent while in the game, and as Codger says, they can go anywhere they choose. I can tell you I destroyed him, but it would not be material as they will be back, and they may or may not be where you last saw them. Just like you they can go wherever they want whenever they want.
No, a player can log off whenever they wish (there's a 15 second wait time if you are in combat) at which point they are removed from the game until they log back in. The player and their ship are gone, the ship isn't still flying around piloted by an NPC.
Yes, it's only possible to see other players while playing in open or a private group, but not in solo. You are still flying in the same galaxy / game world, the modes are simply filters that enable you to see other players or not.