the hose is part of the secondary air pump, don't cap it, but you can buy a little breather filter from any chain store and stick it on the end of the hose, or just find a way to attach it to the intake pipe
for the air sensor I think you just have to make a fitting on the pipe, not sure if it matters where it is but on my Dinan intake it's about right in the center of the pipe
without a heatshield it will suck up hot engine air if it's just behind the headlight, there is a hole underneath the air box that you can stick the filter in, you just have to relocate one of the horns, don't go down to low though, or you'll run the risk of sucking water through the intake and hydrolocking your motor
this thread is referring to modifying a different intake and a different engine, but does have some pretty decent ideas, that's a pretty good spot to mount the filter
http://www.318ti.org/forum/showthread.php?t=14920