Your ship (and station) sizes are restricted by your Ship Yard tech, I think it starts with ships @ 230 and bases in the 670's Get the Yard tech up and your capacity (once you've upgraded the Bases) increases.
That's a tricky one, I've managed it, and I've lost Constructors. I learned everything I know from the forums here.
I wouldn't mind knowing this too, does seem a tad high at times. The Pop-up (as I have it set) for "do you want to colonize XXXX planet" only appears once, so you can ignore the poor quality ones at least.
No, the tech and it's research is handled 'behind the scenes' by Civilians. You get to watch the progress, although I've had stuff nearly-complete get surpassed by other techs. Scrapping ships can help give boosts, but which boost and how that's determined is beyond me.
As to stations, I have adopted the idea of a poster here, I have one BIG base with bare essentials (ie: minimalistic modules) filled with Labs. I re-design all my other bases more or less the same way, bare bones. Helps cut down on over-heat and only have to defend one research outpost. I doubt it's to keep the tech research slow, there's a setting in game set-up for that after-all, you can have nearly any speed of R&D you like.