I recently posted in a thread on starbases that you may find useful.Here.
In addition to what those above me have said...
The radius that appears when you click on a constructor or starbase is the area of effect. This applies from freighter bonuses to ship assist missiles (yes - they really do shoot that far)
As far as I know planets will always provide faster repair than just sitting in space - there is not tech requirement. I do think I remember reading that this repair bonus will be further accelerated if the planet has a starport but that may be heresay.
Here is an example of using the freighter revenue side of economy starbases.
As you can see (hopefully) I have placed the starbases right at the most productive part of the trip. Freighters give more and more cash the further along the route. By placing the starbases (and hence the hefty % revenue multipliers) along the final stretch they start providing large sums of money.
Its easy to mistake the bonus for only 30% However the 3 modules provide a massive 60% bonus as they stack - 10% + 20% + 30% = 60%. So freighters that are passing through the area of effect of all 4 starbases are recieving a 240% bonus to regular revenue.
I should point out that you can only have 4 starbases per sector - I kinda cheated here by building this along an area where sectors meet - thats why I can have 5 starbases close together. The military starbase is to provide ship assist to the guarding fleet. I invested a fair bit into those starbases and want them well protected.
Here is an example of using the starbase factory side of economy starbases.
Yeah thats a hell of a lot of research. In addition to the percentage multipliers provided by the Technological Capital, Omega Research Centre and the Research Co-ordination Centre the starbases provides a further 42%.
The starbases are quite generous as they give a percentage multiplier to both production and research. You may only build one Technological Captital but you are a great deal more free with the economy starbases.
Having a cluster of production/research planets within the radius of a few economy starbases can yeild incredible results. Economy starbases are quite powerful but there is something of challenge in squeezing every last drop out of them through positioning and thinking ahead.
For example you could yield the same kind of frieghter bonus as above while also providing the planetary bonus if you set up your trade routes to pass through your production centre planets... Its one of the rewarding problem solving aspects of the game.