what is the opening circled in Red called, is this an exhaust for the factory air box? has anyone done anything to manipulate air to this location with a homemade scoop-is it worth it?
see attached picture. thank you,

 

MINI calls it an intake manifold, it's the air intake to the lower part of the airbox.

A scoop to direct air to it couldn't hurt. I made one out of some clear tubing from Home Depot when I was running the HAI.