Animal Abusers; Requiring the Department of Law Enforcement to post on its website by a specified date a publicly accessible animal abuser registry of persons convicted of animal abuse offenses; prohibiting the registry from including certain information; prohibiting certain persons and entities from selling, exchanging, or otherwise transferring the ownership of an animal to a registered abuser; authorizing courts, as a condition of probation, to prohibit persons convicted of certain animal cruelty or sexual activity with an animal violations from having certain responsibilities for or associations with an animal, etc.