The effects of building individual labs on your science rate will in most cases not be noticable. If you happen to get a yellow science bonus on your starting planet, and rush buy a lab on it, then you should notice it having an effect in that instance, but thats about it!

In one of my games, i managed to boost the science output of my science capital planet from around 700 to around 4000 using starbases! After that did i notice any nice increase in research speed? No, nothing, never bothered doing something like that again after that happened.

But, i do always set my science rate to very slow, so i imagine higher science rates would be more responsive to the efforts you put in to increase your science rate!

I use the very slow science rate setting so my ships don't become obsolete by the time they reach the enemy boarder! And also to make the weapons in the weapons tech tree slightly more relevant - i say slightly, because even with the lowest possible science rate, i am still skipping huge chunks of weapons tech in my games. So the game could easily use another five slower research rates under 'very slow' and i would use them!!

With regards to your last question (focus): when you set the focus to research, see how the research output of the planet changes (figure with the beaker icons at the top of the screen).

There are 2 main reasons why changing focus doesn't always yield much result:

- either it doesn't change a lot and you will see no effect whatsoever on research time

- or it changes significantly but doesn't make a big difference in your empire's total research output. Remember that to go from for example 6 weeks to 4 weeks research time, you need to increase research output by about 50%