Mercedes 2003 unpredictably shudders and acts like it's going to stall at a stop light, then hesitant to accelerate

I can not post comments as I am too new to this site. I offer this as a suggestion to help in diagnosing the issue.

Have you performed a Battery Reset and Idle Relearn Procedure?

This is where I would start, as it's the most basic possible solution.

Have you ever cleaned the throttle body (or had it cleaned)? First thing, check if your vehicle requires any throttle position relearning procedure after throttle body cleaning and, if so, learn that procedure. Then, identify the gaskets that mate the throttle body to the intake manifold and to the pipe coming from the airbox and buy them, buy a throttle cleaner (carb cleaner isn't good for that, it has to be throttle cleaner and nothing else), remove the throttle body from the car and clean it, being careful not to scratch the plate in any way, then replace the gaskets and reinstall the TB and do the relearning procedure if required. Or have all of this done by someone competent, if you don't feel like doing it.

Reduced airflow around the plate at idle position, due to an excessive carbon soiling of the throttle plate edges, causes what you experience. The smell might be a completely different issue.

Another possibility might be a dirty or faulty MAF.