Trade ports add a flat amount each with no stacking penalty. The longer your "longest trade route" is (hover over credit income to see the line) the bigger the income bonus each trade port gets, even those not part of the chain.

Culture spread stacks (and is divided evenly by number of phase lanes leading out, so if a planet with 4 phase lanes is generating 20 culture/second, 5/second will go to each phase lane). Allegiance gain/loss from culture influence does not stack, but is affected by the difference between your culture output and the enemy's. So, if the enemy has no culture centers and no capital ships in orbit (capitals push back enemy culture), one of your temples should be enough to max out allegiance loss on the enemy planet. But if the enemy has some, you need to build more on yours so that you can generate more culture overall.

Also, having more temples allows it to spread farther and faster from that location. Culture rate is cut each time it passes through a grav well, so where 1 temple at a planet would slow to the point of uselesness after the third (should be third, I think) affected planet, 4 temples would give it enough juice to go a few more jumps.

Hopefully that makes enough sense

Having a desert planet with all trade ports somewhere behind your front line is a great way to make a lot of money so yeah you can "milk the cow" if youve got the space.  I'm not 100% sure how resource focus works except that it's something like the way refineries work.  Instead of producing trade ships and credit income your trade ports start to produce refinery ships and resource income.  I'm assuming the quotas for each extractor are the same for the Advent when using Resource Focus and that it works mainly like the other factions refineries, in which case building one per grav well would pretty much max out the resources you can get from the extractors in neighboring grav wells.  And if youre looking to spread culture faster and through more planets you need to have more than one temple in a SINGLE grav well.  One temple has enough culture "push" to extend through about 3 planets while four will net you culture spread to five or six depending on enemy culture/cap ships, # of phase lanes, etc.  Hopefully you can make sense of all that its a little convoluted

The resource focus is actualy really simple to see how it works. before clicking to acrivate it hover the mouse oer the planet, you see that all of the extraction rates for all of the extractors jumps up once you activate it.

if you have a ice planet with 3 crystal mines each producing 1 crystal a second, you overal production from that planet is 3 crystal per second. if you have one trade port and switch it to resource focus (with a bonus of lets say 25%) all of of the mines will increase by 25%. so now all 3 mines are producing 1.25 crystal per second for a total of 3.75 per second.

Then you build another trade port and activate the resource focus, thats another 25% on the original 1 per second. so you have 1 + (1 * .25) + (1 * .25) = 1 + (.25) + (.25) = 1.5 now all of your extractors are giving 1.5 crystal per second for a total of 4.5

at a resource focus rate of 25% in this example of 3 extractors with 1 crystal per second, every additional trade port using focus give the planet an additional .75 crystal per second.

I think ice planets have 20 logistics slots so if you place down 5 trade ports using focus and have the above mentioned mines each mine will be producing 2.25 for a total of 6.75

I just did another test and that's the way it seems to work. Didn't discover any cap so far. Thanks for alle the good answers you guys.

btw: crystal is really what you always want to have more of, isn't it?

If your running a mod that has sins plus it can give the advent a really unfair advantage. colonize a gas giant, i think they give you up to 7 mines and i think 48 logistic slots. make that your capital and then throw down an starbase with the 2 upgrades that increasee allegence. then with all research you could have 7 astroids giving you about 1.5 a second (base value) pluse 12 tradeports increaseing that by 25% each. giving each mine a extraction rate of 6 per second, or 42 resources per second for the entire planet, and then you get the alegeince bonus for have your allegenince at 150% so you could be pulling in 63 resources per second.

Also there is no cap, as a joke i changed the amount of logistic slots and amount of mines on dead astroids. i gave them 20 mines and 100 logistic slots. i think the planet was bringing in over 150 resources per second.

refinerys. beat all.