B5S4 Adventure

I was replacing ignition coils and spark plugs today, and noticed that a solid plastic hose was broken in two spots (see photos). I followed it to the other end of the hose, and discovered that there's a second break.

Earlier this week, I had the car running with the hood up and hear a sucking noise that sounded like it was coming from near the center of the engine.

a) can anybody identify this hose for me, please?
b) could the break in the T-junction near the top of the engine be responsible for the sucking noise?
c) I've known that I had a boost leak for a while -- I basically get no power from the turbos, though they spin up just fine and the OBDII reader shows I'm getting lots of boost. Could this hose be the source of the issue?

Thanks for your help!

Jeff