If you wanted to do Eve Online's client in html5, how would you do it ?

There are a lot of frameworks and libraries out there and i'm not sure which one to use.

The client will run the same from desktop to mobile, no native stuff.

WebGL would have to come into play, would limit the browser requirements but the only desktop browsers that don't support it are the technologically backwards ones anyway (ie internet explorer). Not many mobile browsers support it unfortunately but a few do (firefox for android does, opera mobile for android does, the nokia N900 built in browser does and the blackberry playbook does. iOS, WP7 and the rest of the blackberry lineup can't yet). I can't see how else you could display much information/any graphics without the potential for very low frame rates

The rest, I wouldn't know, not a web developer

A WebGL 3d engine will be used for 3d graphics/sound.
What about the overall application, such as loading, installing local, resizing per device, GUI, etc..

The correct question to ask here is not "how" but "why."