There's no reason to settle on a specific size at this point, but stars will definitely have to be algorithmically generated. If there is a multiplayer component, that will probably determine the specific size of the universe. In single-player, I'm not sure it'd matter once you get to more than a hundred stars.
I don't really remember the concept video you're talking about, but this does feature a lot of player tuning. I've simply buried it a little: you scale a module to make it bigger or smaller and, at the same time, that changes its parameters. You can also do some module-by-module tuning, such as the way cooling fins deploy, but it's not super-complicated: the challenge isn't to get the ship to work, it's to have a really interesting ship.
The interiors are another story, there's definitely a lot of customization there.