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Okay, well from what I'm reading I don't see any criminal extortion from the messages (i.e., "If you don't do X, I will report you to the police...", etc.).
Digging through your garbage may be trespassing and criminal mischief, depending upon the location of the garbage and whether or not anything is left strewn around your property. But, if you can't prove who did it, then it doesn't matter.
It's conceivable that your child could be charged for solicitation for prostitution as an adult, or the like. But, it could have been nothing more than a joke by a child, too.
This may all just blow over, but I strongly suggest that you stop discussing it online. See my "IMPORTANT INFORMATION" link below for more.
Determining whether a crime has been committed requires a VERY thorough knowledge of all relevant facts, and the EXACT text of the offending statute in the Penal Code. of your jurisdiction. I can't do that in this venue. If you are really worried about the situation to the point where you must know, then you are STRONGLY advised to contact a criminal defense attorney and discuss this in PRIVATE.