Someone else can probably answer that last question, but yeah, the in-game documentation is pretty dreadful, so it's sometimes hard to know WHAT you're researching until it's done. Minaturization is actually sort of a misnomer in that rather than shrink ship components (You have to research the components' own branches to do that), they actually increase the amount of space you have on each hull type. I don't have exact numbers, but it's around the 5-10% range per tech.

check the galciv2 wiki, it provides decent documentation on the techs... https://www.galciv.wikia.com/wiki/Galactic_Civilizations_Wiki