I need to determine what to do with the lines marked in the red and blue circles in the diagram above. They are both marked to the breather pipe, which, correct me if i'm wrong, is that little mess of metal lines going to the stock air intake, which I do not have.

Also, i'm a bit concerned about the line marked in the red circle, I cannot remember 100% (it may have been the line slightly above and to the left on the intake mani) but i'm pretty sure that when was filling the radiator I had coolant coming out of this line (I did not have it going anywhere), which makes me wonder, if coolant is coming out of here how could it be routed into the air intake?

So, block them off, connect them, or just lead them somewhere else?

 

just run a hose from red to blue

 

The air intake breather is actually part of the vacuum system. I think on a stock GSR it connects the air intake to the vent port on the valve cover. For reasons that I don't understand, it's welded to that coolant pipe in the diagram you're showing. The pipes are not connected at ALL. So just connect the water hoses however you want.

 

Ah, I see, I see. Right, the "breather pipe" labeled in the picture is actually 2 separate pipes like you said; the top one goes from the valve cover breather, into the pipe, and into the air intake, then the pipe below it connects blue to red like XREDLINE said above.

Thanks guys, very clear now.

 

Like gagnar said, they're not connected to air, just two welded pipes.
Connect the two, done.