Someone has been forging letters to my children's schools in my name. How can I put a stop to this?
Forgery is a crime in pretty much every jurisdiction, so you can take your concerns to the police. School officials may be reluctant or unable to disclose information to ordinary citizens, but police can typically obtain more information (and may know things relevant to the case that you don't know). However, they may decide that there's no way that they can determine who the perpetrator is. At a minimum, having a complaint officially on file could be useful.
If a person forges your signature on a contract, when the other party comes to sue you for breach of contract, you can defend yourself by showing that you did not agree to the contract (as in, it wasn't you), which might involve calling on an expert to testify regarding your signature.