1. Does it make sence to build a space port (dock) on every planet/asteroid to increase $$$?
Trade ports, yes. Refineries yes... but refineries have diminishing returns.
2. What does a white line mean when hower over the $$$ indicator on the top of the screen?
Thats the longest available trade route -- an unbroken chain of planets with trade centers. (Please note that uncolonizable systems don't break the chain, but any colonizable one, even a mere dead asteroid, will unless it has a trade center).
3. Does it make sence to build refineries in each planet/asteroid? Do they "work" together and between planets or is it a planet specific improvment?
Yes build refineries. I believe asteroids give you a report on how many refineries they can support, and how many are being supported. Don't go over the support limit.
Refineries appear to support one jump "out" from them, so yes they are inter-planetary, but they don't work together like trade centers.