Whirring noise and constant high reving

SOURCE: noise when car is started

Sounds like the starter stays "sticked"on... Check the starter relay or after the sound goes away touch the starter for heat. If its too hot it means it stays on working even when the engine is allready running...

SOURCE: exhaust light on 2004 VW touareg is coming on.

try the lamda sensor on the exhaust it may need cleaning or replacing

SOURCE: Smoke sometimes out of exhaust bypass

It is not an exhaust bypass or filter.

It is a booster heater , which enables quicker warm up in cold conditions.

An electronic box and sensor only kicks heater on when subzero conditions.It burns diesel , hence the smoke from underneath passenger side.

Hope this helps.

SOURCE: on start up bit like exhaust blown near air box

If you have a Turbo charged engine the gaskets on the turbo are probably the culpirt. If you can lift and support the car on jack stands. Remove the lower shield from the car and inspect the turbo. You may have to remove the right frount wheel and any sheilds in the wheel well to see the turbo. The Turbo seals require relitivly high engine RPMs to seal properly. The Turbo starts to work about 1500RPM. Is it Gasoline or Diesel? The Variable vane turbos used in most USA,VW's after 1999 will start to work slightly earlier. The type of engine oil you are using, is it up to WV specifications could also be a factor. Not all synthetic oils are alike.
Upon inspection look fordark grey/black sooty deposits indicating where your leak is comming from.

SOURCE: 2000 Beetle Loud Whirring at start up

its your secondary air pump. it turns on in the cold morning to inject more air into your exhaust, something about emission. its normal to be high pitched. once on my car it was way loud, i looked and the hose had disconnected. either way its normal if its not super loud. but if its everyone is looking at me loud then check for loose hoses!