#1 - Roughly you're fairly limited to what portion of the Civilian Economy you can influence, but you can influence it.
First, the Private sector is going to build x amount of ships per Colony/Spaceport (initially, may be more late gate).
Obviously the more Colonies/Spaceports the more ships they're going to build.
These ships need something to do, so you need to build Mines for them so that they have jobs.
Essentially, the more Mines the more work, and the better the Economy generally runs.
I try to make sure there is a Mine for each type of Strategic resource as close as possible to each Colony for a number of reasons - supply being the biggest.
There is another big reason for having resources nearby, and that ship range.
They can't get the resources if they don't have the range to reach them.
Another impact on the Private sector is State and Military ships.
For one, keeping these fueled keeps the Private sector busy.
Building these ships keeps them busy as well gathering the resources.
I haven't been able to confirm this, but it seems when you have more Military ships (to a degree) the Economy runs better - not sure if it's a supply, safety, or what type of issue, but it seems to hold.
#2 - You can look at your Colonies screen as well.
Under the "Cargo" tab you can see what is stored at that particular planet, and if you have a Spaceport at that planet, these resources are effectively what's available at the Spaceport as well.
I Mine the heck out of Gas Planets (fuel) in and around Colonies to help insure I have ample fuel supplies at that location.
Don't forget that there are two types of fuel, Caslon and Hydrogen (later).
Personally I put State ships on Hydrogen and Private ships on Caslon, but you need to be manually designing/upgrading your ships designs to do this.
The benefits are many.
You're less likely to run out of fuel since you have two types, since if everything is on one type it's very difficult to keep everyone supplied mid - late game when you have hundreds/thousands of ships.
Also, your Private sector is busier since it needs to keep additional resources stocked.
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