re: Research Stations - absolutely, yes. Go to the research tab and click on the far right-side tab showing all your research stations. Seeing you're asking this question I'm guessing you don't quite understand how research works, and it's a bit lengthy to explain, but important.
The number to understand first is the one on the right, Total Empire Research Potential. This is your combined research cap for the three types of research. It'll grow as your empire grows (tied to population I think, but grows logarithmically, so it'll slow down mid-late game). Now look at the three numbers next to Total Research Capacity. This is just a sum of the numbers above for Weapons, Energy, and High Tech research. (before upgrades, each research lab component gives 20K research potential, to a research station with 120K has 6 labs) But often you can build research stations at locations with bonuses, or have a race/leader/scientist that gives you a bonus. This modified output is shown in Actual Output.
Another thing to know is what happens when your Total Research Capacity exceeds your Total Empire Research Potential. Before bonuses are applied, each of the research totals are proportionally reduced to fit the empire cap. Then the bonuses are applied. Thus, your Actual Output totals can exceed your Total Empire Research Potential - in fact, you should make sure they always do, by at least a little - this way you're always getting the maximum amount of research your empire can produce.
To answer your original question: absolutely, yes, you can skew your research potential towards one area, and in fact early game it's highly recommended you do. For example, in a PreWarp game, it's a valid move to dump every last drop into Energy to get hyperdrive tech ASAP, with maybe the exception of 20k for the other two that comes default on SSPs - maybe you'll get a lucky crash and get a tech or two done.
re: Energy Collectors - they are a surprisingly important piece of tech that can easily get overlooked, especially in your first PreWarp game as you won't have them on anything by default. Provided that the ship/station they're installed on is stationary and near a star/black hole/etc., they'll generate power for 'free' e.g. no fuel needed. This doesn't seem very useful until you consider that a lot of modules, especially those related to mining, construction, or research, have a static power draw, meaning they constantly suck energy. It's not much, but for a distant Mining or Research Station, it'll bleed the fuel bunkers dry, and the station will do nothing but cost you maintenance until some Private Sector ship finds the time to resupply it - and then a few months down the road it'll happen again. Energy Collectors (solar panels, basically) are crucial to cover the power supply of pretty much any stationary structure you build, and are useful for constructors too for the same reasons. For ships, on the other hand... most don't have much static power draw, and I don't keep mine idle often, except maybe isolated defensive fleets. If you tend to keep your fleets idle and are annoying to return and find them mysteriously low on fuel, try adding an energy collector. Otherwise, don't bother, they take up valuable space.
This allows the base to use energy from fission/fusion reactors to create fuel, and power weapons, shields, etc.
Whoa there, you were doing so well until you mentioned turning energy back into fuel. That's a super-uber-late-game tech that requires a special component. I take it you like super-long games?
re: Spaceports - your gut was correct in this case, spaceports can only be built at colonies you own, unless you're playing as a pirate - as an empire you can find abandoned ones in other places, but they're not near as much use without a planet below. Defensive bases can be built at any location, however, if you want some serious defense at a given location.
Going by the default designs, each step up the spaceport size ladder increases:
-number of docking bays, used by freighters and for refueling
-number of construction yards, used to build and retrofit both private and state ships
-number of research labs, which give you research potential
-number of weapons, to make bad things go away/die horribly
-number of shields and armor plates, used to avoid losing your expensive space station while the weapons do their thing
-number of cargo bays and fuel cells, for boring logistical reasons
and oh god I had a lot more to this post, but the my login reset inexplicably and you can't recover it on this forum implementation. -.- Lucky I crtl-A'd this much. I'll retype the rest later...