This sounds like it is a non criminal citation. Likely there will not be a greater penalty if you pay versus going to court and losing. Bit if you go to court and win then there is not any penalty. Also, note that the merchant can pursue civil action too. That may be incentive too to fight the ticket. Good luck.
You can go online and Google the elements of the offense for the crime. Also you can look at the legal guide I put out a few days ago on 9-5 re: a basic overview of "conspiracy". You need to get a lawyer. I think you are the person that has asked a lot of questions on this forum already and it seems that you are trying to handle on your own something that you should get help with. Don't be foolish. Get a lawyer.
The first answer is generally correct, but because CCAP is a WI program that has a variety of input notation possibilities it is not possible to answer your question 100% without knowing the basis is for the dismissal to begin with. You should talk to an attorney in your area that can looking into the specifics of your case to be able to tell you whether jeopardy has attached to your case or not.
Ms. Missimer is correct. Just to clarify, the ethics rules consider the Public Defender's office as an entity to be a law firm. So the State office could at best only handle one of your sons' cases. Having said that, it is possible that you are being told that there is a conflict when there isn't one really so that the cases get assigned out for any number of reasons. Hopefully your sons will get good counsel.
From your description of the events you have a civil offense not a criminal one. Given that it is not a crime you will not have to say that you have ever been convicted of a crime. If you were not printed and photographed then you have not technically been arrested either, just cited. Good luck.