Delete the "DcBrowser" folder (make a copy of it in a place you want, your extensions are there) located in the "C:\Documents and Settings\<username>\Local Settings\Application Data\" path and run the browser again. I don't get those connections you say and maybe disabling extensions doesn't prevent them to connect to the internet. The only connections I get are internal plus a external connection made for the autocomplete service of the URL bar of the default search engine you selected. In this case the default search engine at the very first run is Google so a Google connection is expected.
The cause is that in normal Chromium builds the New Tab page is located inside the "resources.pak" file, 360EE has the New Tab in an external file called "newtab.zip". New Tab extensions on 360EE won't work.
This seems to be a SwiftShader thing, maybe manipulation the browser with flags could make the maps display but unfortunately I don't know which flags to use.
If you go to "chrome://history" there is a "Clear browsing data" button at the top-right corner of the screen, I tested it and it cleared the history. Also, all browsers store history, 360EE does it as well.