Research is civ-wide (you only research one tech at a time), but each planet uses its own industrial capacity (factories) to build its own improvements and ships and has its own economy. Whether or not you're breaking even on a planet by planet basis is largely irrelevant so long as your civilization's economy is staying positive, and the exception to the idea of the planetary economy is that you can only set the tax rate for your civ, not each individual planet.
You can specialize, but the problem you may be running into is that of your spending sliders. Firstly, the research, social, and military sliders are all at 33% at the start of any new game-and the overall production slider is only at 67%. This means you're getting a total of 0.67*0.33 or 22% out of your total in each category-for a civilization capital this means 5 research, 5 social, and 5 military (the latter two of which won't do you any good unless you're building something) whereas an initial colony would give you 3 research, 3 social, and 3 military.
So the answer to your question is that you want to ensure that you're funding the appropriate buildings at the appropriate times (which varies by player, game, and playstyle) and perhaps more importantly that you have your overall production slider set to 100%, even if you don't have one of the other three sliders set to 100% as well. (A 50/50/0 split seems to work fairly well for new players; concentrating on only two areas at a time is much easier than three. 100/0/0 splits are used as well, but this is actually considered an advanced strategy because most who use it tend to try to meet all three needs with it, rather than just one at a time. You're more than welcome to try running at 100/0/0 for short periods of time to see if you get more done that way, though.)
For the other half of your question: If you wanted to have a planet with all factories and a planet with all labs to get anything out of both of them simultaneously you'd need to run some kind of military/social funding (probably military, if you don't need to build anything there anymore) along with some kind of research funding-a 50/50 split would work. However in this instance you're only getting 50% of the maximum capacity of each of them. But that's a discussion for another day.
The economic capital is misleading...a boost to your economy is always welcome, but it is essentially the equivalent of two stock markets and as such its placement is not overly large of a concern.
Which version are you playing?
