You probably need to go design some engines. Unlike most 4X games, successfully researching Nuclear Pulse Engines doesn't give you a generic "Nuclear Pulse Engine" to add to the design. Instead it gives you the option to design nuclear pulse engines (with all the other modifiers eventually available to you such as fuel efficiency, thermal reduction, hyperspeed capacity, power efficiency/inefficiencies, etc.)
AFAIK, you can add/remove traits on commanders because they have zero game effect, just RP fluff.
As far as the Governor showing unassigned, sometimes that screen doesn't update properly. Try exiting the commanders screen and going back in to see if it changed.
I was bummed to find that my idea of using geosensors on missile/drone-delivered buoys won't work, because you can't target planets from distance.
I understand why (because otherwise planetary sieges would be non-existent...you'd just bury enemy planets in a long-range enfillade of missile fire) but it still stinks. I could make a design that would manually drop sensor buoys at the planet, then scoot off to the next one, but that defeats the primary purpose to the missile-delivered sensor idea -- keeping my scouts safe from lurking Precursors and whatnot. I suppose I could design a scout cruiser/carrier that would carry recon "fighters" with a single sensor buoy on a railmount....hmmm.....
Oh, and government type actually affects a number of things. One of the most practical and immediate things it affects is how active the "corporate sector" will be, based on your Trading attribute (Shift+F9 to view your race's traits). Hive Mind is a -30 to trading....you won't see much commercial activity if any. Corporate Government adds +30 to Trading. You will wind up with multiple shipping companies, mining colonies galore and LOTS of merchant shipping traffic.
Also affects the total enemy ground strength needed to force a planetary surrender (based on Determination and Militancy ratings). But since I've never seen the AI launch an invasion, that's kind of moot.