I actually believe I have found some answers. From discussions and experimentation this is how I belive it works.
Yes, you can only have one research effort going on across all you planets, even if you never researched "Intergalactic Research Network". (seems odd from a real-world view, I suspect that it is to control research rates)
Each level of "Intergalactic Research Network" adds one lab to the network
I.E. Level 1 gives the research power of the two highest labs in your empire, Level 2 gives the research power of the three highest labs in your empire, etc)
All of the labs on the network must be at the level needed to be able to research the "Intergalactic Research Network" (level 10).
So, to labs at level 10 with IRG should give you the speed of one lab at level 20 (I was not able to try this).