The sizemod associated with ship modules is based on the unmodified capacity of your ship.  It wasn't always this way, which meant that miniaturisation was a hit and miss affair, but it works fine now.

Miniaturisation doesn't really make components smaller it just increases ship capacity for all components (which is kind of the same thing).

The bonuses to abilities like military, social and research production mean that a percentage based on the unmodified number is added.  Depending on your race selection you may start out with an ability that already helps you out.  Bonus production (manufacturing or research) is important because it is budgeted separately from base production, and it only costs half a bc to fund a point of bonus production, compared to 1bc for a point of base production.  Simply put, it makes you more efficient (use less credits) at that type of production on a civ-wide (abilities) or planetary scale (starbases, buildings).

Bonuses to social affect your production counting towards building on tiles down on a planet, which bonuses to military affect ship building.

So far as approval and morale are concerned, check out the wiki page.

Trade routes, once they're set up, don't need a lot of maintenance, unless your freighters keep getting shot at and the route closes down.  Usually it's not worth re-opening trade until conflict has passed.

Starbase upgrading can be automated, and you can set a rally point on a starbase to send constructors to it without requiring your intervention.  You may want to optionally uncheck the boxes which prompt you to build and pay for a module in the options screen, meaning even less for you to click on, personally I prefer to pick the modules but not get prompted about paying for them (though, if your treasury is low you will always get prompted).