is it possible so i that can set up a secure webpage in which an authorized web user could edit a javascript file from their bowser, and save it back on to the web page?

No you can't

Well, you can edit a javascript file or any other file in a browser page and save it through the web page to your server. You'll want to use php or a similar language to save the file on your web server. Lots of web hosts provide File Manager applications to do this.