It will cost a lot more than $250 because as you say there are court fees and you will probably want supervision which will add extra. I would...

What should I do in my situation?

if you are suspended for DUI it's more serious. Even at that why you were suspended can matter.

Unless it's a camera ticket, it is am moving violation.

Correct. If it calls for a blow you must do so. You get a letter from the SOS alleging that you refused a rolling retest. Explain what happened....

Can I receive damages from the court, circuit clerk or city for negligence?

Highly unlikely. Public officials enjoy immunity from the negligent performance of their administrative functions.

Will I go to jail?

Speeding does not require knowledge or intent. You need a lawyer. I suggest Mike Wepsiec.

No. this is an error that the state can fix.

My license was revoked in 2011 after the arrest in 2009. It was an accident that wasn't my fault but i was arrested anyway.

It makes no sense to you because you don't understand the license hearing process. Once you plead guilty in court, you have been proven guilty...

More expensive in Chicago and Joliet. Those of us in Springfield are blocks from the nerve center of hearings

Potential jail time though not likely. He could lose his GDL too. You should consider a lawyer