1 - There is nothing wrong with "cookies" but html5 web storage has a lot more flexibility when it comes to storing data in the browser.. It also works better with many modern mobile devices (and mobile devices are becoming more and more popular on the web today).
2 - You're correct about #2 - Caching as much data that does not change in the browser (such as images, common requests etc) will often improve the user experience -- especially when on a poor connection such as a 3G mobile phone.
3 - CORS is defined by the w3dt.net servers .. the main w3dt.net site does not allow "cross-origin" sharing to my knowledge but sub domains such as "results.w3dt.net" do allow CORS so that users may embed results into other websites. -- Read here for more info: http://en.wikipedia.org/wiki/Cross-origin_resource_sharing
Have a great day :)