The government would have to prove that a crime was committed and that you committed that crime. Your statement alone, without ay further evidence, would be able to be subject to a corpus delecti motion (govenrment has to prove the body of the crime) and the charges may ultimately be dismissed if the statements are the only proof.
Your public defender should be able to review the discovery, all of the information that the State Attorney's Office plans to use against you, and be in a better position to mitigate the plea offer from the prosecutor. The prosecutor can always revoke their offer up until the time that you plea the case out.
Since obtaining a green card is a privilege and not a right, you may be tested for drugs. I think the less that you tell them about past drug use, the better. Answer questions that are asked of you honestly, but don't provide more information than that is asked of you.
Usually your rights to an attorney extend when questioned by a law enforcement officer. If the public servant was not a law enforcement officer, then I don't think you would have to be informed of the right to have an attorney. if the public servant was acting on behalf of law enforcement, that may change things. Anytime that you are in custody (not free to leave) and being interrogated, you should be told of your right to an attorney.
Either way, it is inevitable that you will be taken into custody. If you are locked up on the probation warrant, your failure to attend the arraignment would not be your fault as you would have to be transferred for that court date if in the same county.
I would contact the police in that jurisdiction and file a police report if this hasn't been done already. If the State Attorney's Office dismissed the charges, go to the higher ups at the Office and demand that the charges be refilled if they truly have merit.