Originally Posted by Monooxide

If you're looking at the engine bay from the front, the wastegate is the round silver item to the left of the intake with a blue silicon hose going to it. This actuates a arm which opens a flapper door and allows the exhaust gas to bypass the turbine wheel in the exhaust housing to maintain the boost pressure that the wastegate actuator sees through that blue hose. This is all considered an internal wastegate, attached to and integrated to the turbo.

Another style of wastegate is an external one that is mounted inbetween the turbo and the engine and mounted on the area where all the runners of the exhaust meet together and enter the exhaust housing. This also has a silicon hose on it to control the boost pressure by opening to allow exhaust gas to be routed around the exhaust wheel and maintain a boost pressure.

The reason it takes a while for the turbo to spool up is because the engine has a shorter intake manifold, probably higher duration cams and a larger turbo. If you were to go back to a stock intake manifold you would see faster spool and a little less top end power but more in the mid range.