1) Is there any way to develop for the Xbox 360 using HTML5/JavaScript? It can be either fully browser-based, a server hosted application, or a native C#/C++ Silverlight wrapper over HTML5/JavaScript code (like UiWebView on iPhone or WebView on Android/Google TV). I have no experience with this platform, so please accept my apologies for what might be obvious questions.
2) Does anybody know how powerful the Xbox HTML/JavaScript/CSS rendering engine is? Is it Webkit based?
Unless you have access to some NDA development tools that the rest of us don't know about, I can confidently say that there is no way to develop for the Xbox 360 platform using HTML5/Javascript/CSS.
If you have access to the professional development tools, perhaps, but that's all under NDA. You'd need to refer to the documentation and the information on the developer portal.
You might be able to build some sort of rendering implementation using the XNA Framework, but that'd be a lot of work. (See also: this Stack Overflow answer)
Due to the NDAs surrounding Xbox 360 development, we simply don't know. If there is a rendering engine, it's almost certainly trident-based (and definitely not using Webkit).