Everyone is correct, if the courthouse was closed you couldn't appear, even if you wanted to or were able to. However, you should inquire as soon as possible as to when it is rescheduled to and make sure you appear on that day.
You definitely need to talk to an attorney about this situation. Your version doesn't state any reason given for the stop and search, so it could be a bad stop. Your attorney should obtain the police report and then advise you based on that and your version of the facts.
Your question does enter to the civil law area of a suit for defamation and consulting an attorney experienced in that area is best. If these are in fact lies, then evidence of the truth will be very important.
Well, it is never to sign a paper admitting anything without the advice of an attorney. That being said if the police did not arrest you and charge you then there will be nothing next. Also the stores will not collect these fees so you actually gave them a benefit by paying the money. It would be unlikely that you would receive a summons if you were not arrested.
Your fiance should discuss this with his lawyer. If he is not satisfied with how his lawyer is handling his case he can request a new lawyer. This may delay things a bit, but better to have someone he has confidence in.
Someone needs to testify to this information if the defendant themselves does not testify which in many cases they don't. Having someone else putting this information on the record is difficult as it is not generally considered relevant to the charges. Discuss this with your lawyer as their experience will be the best guide for you.
You were not convicted and this should be sealed. The arrest might show up as a past situation, but should not ultimately prevent you from entering the country. You may be scrutinized more than some other entering the country.