About giving noobs designs why not:
1. Make encounters and certain missions that give you a chance to find random ships/ship designs? (this can work for older players to) the ship designs could range to a small, weak swarmer to pships. They could be good ship designs to, (like million, or billion fleet power) so noobs have to save up and older players would benefit from it to.  like the encounter with the derelict mothership you could make a encounter/mission about exploring ship wrecks and sometimes, you could get a ship (and design obviously) "your crew is able to fix the ship" or something like that. Or just the design "Your crew found blue prints to the ship but it was beyond repair."

2. Make a tutorial on how to make good ships

I think both ideas would help noobs and older players.

I think your asteroid base and mothership should have some sort of defense, like space stations. Maybe you have to research it or buy it, or maybe it's missiles and fighters like the space station, but I think they shouldn't be defenseless.

I have an idea. What if you could buy a hanger for fighters and crap on your ship. Maybe have fighters and bombers available to buy. Fighters being more for attacking other fighter and bombers, but can damage regular ships to. as to bombers, who damage ships more but can fight fighters, just not very effectively. Fighters/Bombers can add a little extra power to ships, maybe not show up on fleet power. that's all I got on the idea, maybe someone can help expand on it.