i have been wondering what this hose is. pulled out the foam inside, and it was sucking air in. my idle moves from 600-900 rpm or stalls after car warms up. the 4th pic is of BAC. air hose is kinda bent going from elbow to intake. thanks.

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That is the intake for the air pump. Emissions related.

 

it goes to the airpump

 

would it mess with idle at all? would the bent air hose on BAC mess with anything?

 

The airpump intake has no effect on idle.
Your BAC hose looks pretty normal to me.

 

That foam looks like its to thick to let any air through. Keep in mind that the air pump supplies the air to acctuate the VDI and 6 Port setup on an s5. It also send air to the cat and withou it it can kill a cat. Leave it out for now and find a little filter (autoparts store) for it and your car will be happier.