As I understand cocos-html5 at least for certain browsers requires web server. How do you deploy games on mobile devices (I’m mostly interesting in android and win phone)? Do you use a web server running locally?
No, usually we deploy it in a internet server, no local server.
If you want to run it as native app, you may try Cocos2d JSB. It will pack your game into a Hybrid app, and then you don’t need any server.