Setting auto-search to 1 for all ItemTypes will probably not work so easy. You will have to skip all core itemtypes and there are a few where it´s more recommended not to use this setting cause of performance reasons.
Filter is used for searching a particular table entry. Don´t use '' or "" for searching, e.g.:
.../server/odata/User?$filter=login_name eq admin
Parameters to a Method can be passend within the body. This sample worked for me: https://community.aras.com/b/english/posts/server-side-methods-with-the-aras-restful-api
But why use REST for this use case at all? You can directly run your Method from the editor. Just ensure that you are the only person to access and execute, or just use it temporary.