First, unless you know for certain this cash buyer individual broke your windows, I would disregard the event and not associate it with the cash buyer. Obviously, if it was him and he was caught, he would be facing pretty serious property damage consequences not to mention risk losing the purchase contract. Don't ever mention to him you suspect him in any future conversations...in fact, if the opportunity arises, Say it was kids, play it innocent and casually mention the police have been notified and they are on watch for the property because this has never happened before.
Assuming it is the individual, this seems like a scare tactic or undue influence on you that you have the choice to disregard. You don't have to sell your property to anyone. Unless you are in a situation that you need to work with this individual to negotiate a higher price on your behalf or take his offer, I would decline the offer (its too low anyway, right), make a phone call to the police about the broken window incident (putting them on notice) and sit back awhile.
I have found in my experience (broker in three states) that cash buyers are either very serious about the property or not, they are not in the middle. He either will go away or come back with a higher offer.
I don't know if that helps, but that's my experience. Happy Holidays.