Possibly the V4 Architecture document I just posted will clarify.
I don’t foresee any of the components being web servers. It would be awkward to use a web server for any of them. Web services don’t have much in common with a general purpose web server beyond using HTTP as a communications protocol.
As for what needs to be running—it’s not much different from now. The public game server for V3 needs to be running continuously, as does the web site if anyone is going to download anything from it.