I've always thought that the URL to use when searching articles is the same you would use when retrieving a collection of articles, just with the search terms or filters included as parameters, ie, /articles?q=terms
Approving articles could be as simple as posting TRUE to the "approved" attribute of an article, ie, /articles/1234/approved
You just need to make sure that every resource that can be modified or retrieved has a URL.
That could be done; WebDAV introduced several new methods to HTTP. The drawback is that your clients lose the ability to use standard HTTP libraries to talk to your service because you're using a non-standard set of methods. The 'Uniform' in URI and URL doesn't just apply to the resource identifiers; in a RESTful system the methods and representations both need to be uniform as well. That allows general-purpose clients to be able to interact with the service, and that was what made the web take off when earlier FTP and Gopher systems did not.
Approving articles could be as simple as posting TRUE to the "approved" attribute of an article, ie, /articles/1234/approved
You just need to make sure that every resource that can be modified or retrieved has a URL.