I have installed Mono under Apache and its working.
My question is - Do I need to restart the mono service each time I make ANY change to any asp.net file under Apache, be this a .cs or even a configuration change in web.config?
Yes. Mod-Mono only clears its dll cache when you restart mono so to see your changes requires the restart. You can also configure an auto restart.
There are some helpful hints at: http://www.mono-project.com/Mod_mono#Control_panel
No, if you change web.config, aspx or code-behind files you do not need to restart apache/mono-server. Only need to restart if you replace other assemblies that you deploy precompiled.