The distance from the capital doesn't matter for trade port income. However, I'm pretty sure that trade ports outside of your culture make less (though I'm not 100% sure about that).

The longest route bonus is figured by taking any two planets you own and finding the shortest trade route between them (if one exists).  Repeat for all planet pairs.  The longest of these shortest routes is your "longest route."  Confusion over the term "longest route" comes from the fact that there are certainly longer routes visible, but there aren't any longer "optimally short" paths between any two worlds than the one calculated. 

The bonus given by the longest route affects all trade ports, whether or not they are along the longest route itself.  Thus, it is generally worth it to place as many trade ports as you can, except in the case where placing a trade port creates a shorter path between the two planets that currently are on the ends of your "longest route."  It gets a bit complicated though.. to really figure whether it is worth it or not, you have to weigh the slight loss to all trade ports from a shorter longest route compared to the increased income of having more trade ports.

My general rule is to first place trade ports along my planned longest route and get that established.  Next, I fill in any worlds that don't shorten the longest route.  At that point, once all logistic slots are used on all those worlds, I consider filling in any remaining planets.. considering that you also have to build research structures it makes sense to use so called loop worlds for that purpose. 

Lastly, consider building starbases on uncolonizable planets for trade only if it will extend your longest network (that is, it will connect planets in such a way that one pair of planets has a longer shortest path than your current longest path).  The investment of a starbase is vary rarely worth the expense if it is only to be used for trade, even when it does extend your network.  The only time I'd consider putting a trade dock on a starbase (in a competetive game) is if I built it to protect a front line that has since moved outward and I have extra cash, have built all other trade ports, and the starbase still has an empty slot.  In all likelyhood I'm already winning such a game so they don't ever factor into gameplay in a meaningful way.

So, just to clarify:

If I already have a route (lets say 7 planets/links long) in star system 1, then I jump to star system 2, I can put up 3 or 4 TPs there and collect cash from them?  Up to now I had been making as long a link as possible, then not building any more tps, even though I might have 2 star systems that are unattached to my trade route.

Do I have that right?

RM

Yes RM. The trade ports in system 2 will benefit from the bonus that was created in system 1. However, the chain will not travel between systems. All trade ports receive the same income* regardless of their position on or off the route. The length of the longest route only determines what that income is.

* Culture and planet bonuses can modify income. Also Starbase trade ports are different from regular trade ports.

A tip for creating trade routes is to put up a trade port and then hover on the credits income.  Itll show the longest route.  If its the same or longer than the original, allow the trade port to be completed.  If it breaks / shortens your longest route, cancel the trade port before the drone even begins construction.  This traderoute update doesnt occur when upgrading a starport, though.  Just the actual trade ports.

Thanks, that is what I call a good answer!

It will if you have a starbase with a trade port around each star.

Yes same thing for wormholes, the trade route will go through wormhole if you base on both ends.