Ideas are always good, even if they seem like they'd not be possible. They just force me to figure out creative ways to make them happen if I really like them.
Anyway, on to your specific ideas... Its theoretically possible to set something up such that you'd be able to chat outside the game. The only problem with this is that it'd be a mess to those in game (since any messages would likely show up like NPC messages (and thus wouldn't have any way of identifying easily who sent them)). This is more of a limitation of the game itself than the server. However, it would be possible to have an email like system built on top of the simple mail system in the game. It'd be limited, but possible. It'd also be possible to have the server save any simple mail that is sent to you while you're not online so you could view it on the website or something like that. I was actually considering implementing something like that in the future (although, its not high on the priority list right now).
The problem with the second idea is that the server doesn't have any idea about character information unless you're online. Even then, only the ship server that you're on knows about it (and the ship server itself doesn't have access to the database to store anything). Having it so you could see your current character's information while you're actually online should be possible, but it would probably not be very pretty to implement. I'll keep the idea around, but I won't promise anything any time soon.
External team chat would probably be easy to do, since that looks/acts more like an IRC like thing than normal chat in game. Of course, that requires BB support, which I'm not reimplementing any time soon, likely.
