Althouth you are limited at the moment towalking around your bridge, I'm pretty sure they will add to that soon. There are places like DS9 to visit (complete with the wormhole) and not only is your character fully customisable, so are your bridge officers!
NOTE: I was replying to your message title, not what you posted, You have 3 character slots at launch, and I think you can buy additional slots later. You can visit Earth Space-dock, I can't say I've been to Earth, but I'm not very far into it yet. - Time travel, I think so. - Not sure about ships and phasers from other eras.
There is a mission, and maybe more, that does involve time travel. I've never tried to go to earth. I have been to Vulcan, that's all I've tried so far. There are a lot of weapons, if there are ones that look like the old ones, I have no idea, I don't really pay attention. You have a lot of design choices with your ship, I imagine you can make it look like an older model, I am still new to the game, so I haven't been able to mess around much with it.
"Sigging yourself is the best way to make sure everyone knows how narcissistic you are." -Xiahou Dun
You can walk/look around your bridge, and that's it for now. You can visit familiar planets. And you have many many options for the uniforms you and your crew wear.
And how do the characters work.. you create one and that's your guy for good?
Yeah, basically. You create a guy, and that's your guy and you're the captain. You get different bridge officers (computer controlled teammates) along the way. And like somebody else said, you can have 3 character slots, so you can create a few different characters to play with.
Can you visit earth and san francisco? Time travel to 1985? Visit any famous ships from Shatner era Star Trek? Change uniforms? Get different phasers from different eras?
You can't actually go to Earth at the moment. The closest you get is Earth Spacedock. So far, I've played one mission that involved time travel. And you do meet a few Shatner-era ships then. There are a few ship classes you can use that are refits of the shatner-era ships (Miranda, Consitution). There are lots of different weapons, but they are all from the current era (but I guess some of them could look like older-era phasers.
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