A question on game mechanics

I am not sure how "precisely" this is, because they seem to get applied in various ways.

Logistics gains are clear, as they are purely additive.  That is, if your logistics was 9 and then gains 6, the max fleet size is now 15.

Fairly easy are the bases.  It is my understanding that the stated percentage gain is applied to overall tax revenue, social construction rate, military construction rate, and research points generated.

I am a little less sure of precisely how the influence one is applied, but I think it is done similarly  That is, a value is generated based on population and stuff and then applied to that.  I think a race value is generated that includes the stuff in game race setup and the new addition added to that.  So, if the race had a 10% racial bonus, the 110% value would be a factor in the math.  The 39% gain from a maxed out base would make that value become 149%.

Cloudier is how morale/approval is calculated.  I am convinced that the gains do happen, but I have never explored the equation to see how the change factor fits in.

Another area I have never "gone under the hood" with is miniaturization.  It might be a percentage of the original hull size, but I am not sure.  That is, a cargo hull might be base 60, and each miniaturization gain might be applied to 60, such that a 15% gain yields 69 and another 15% makes it 30% to 60 for 78.  You could easily test this one if you want precision.

You could avoid resource anomaly starbases by preventing anomalies in the setup, I think.  The AIs research and use Trade, so that would take a mod, if it is possible at all.

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).

Going Evil also helps keep base stuff simple!