At the moment to stop JSCover server I go to http://localhost:8080/stop.
What are other ways (commandline or not) to stop/restart JSCover server, in case one needs to apply some configuration changes and wants to do it in automated manner?
None really, except if you run JSCover as a thread in a Java application (such as shown here).
You could put in a feature request at https://github.com/tntim96/JSCover/issues if you can describe exactly what you need and think it would be useful to others.