A school has no right to issue a citation to anyone.
If only the police were involved...
As for the rest, all we have is a statement from police, not confirmed facts. Their statement shows a few inconsistencies.
You can see if someone is inside without opening the door, and unless/until you know it is not a school vehicle and that the owner does not have permission to plug in, you do not have evidence of a crime in progress. You can be charged with trespassing even if you were only verbally notified that you are no longer welcome.
Police can do a search for evidence when they have reasonable suspicion of a crime, but that search must be related.
Well, that is easy. If the minimal cost of processing a misdemeanor is $100, it doesn't mean that you can go about and commit $99 misdemeanors all you want. The society wants to prevent such behavior, no matter the cost.
No, but it does mean it makes a lot more sense to issue a citation. It's much cheaper and still makes repeat offenses clearly much more trouble and expense than it's worth for the offender.