The part in the first picture thats bolted onto the intake manifold is the one I totally removed. Motor will die on decel from high rpms on occasion but not enough to bother me honestly. I may put it back in, but you can definitely remove it for testing purposes. You will have to block the hoses off.
The ACC or IAC, I don't remember what the FSM calls it, is whats in your hand in photo two. The plunger/springs contraption should move freely. You can unscrew the solenoid part from it and blast all the carbon out with brake kleen. Took me a bit to get mine working so it moved freely.
Evan