Blizzard will absolutely work with legitimate law enforcement requests for data, logs, account information, etc. They do respond to police and law enforcement requests.
When you ignore someone, you have to do it from each one of your characters. That should ignore the entire account of the person you don’t want to talk to - for that char of yours. It should also ignore their in-game mails to you. The exception may be if they are on an different server and it may not properly ignore them.
You can read all about how Blizzard handles harassment here, and how to put in an ongoing harassment ticket.