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In the previous iterations IE is actually a fork of IE4 which they add features to, so it has no relations to normal IE.
So IE7 is probably just some 'feature equivalant' to IE7, whatever that means.
I don't think so.
From what I've heard, the browser in Windows Phone 7 is a version based on IE7 with a few enhancements from IE8. So, I'm pretty sure it's based on the desktop IE7 (with modifications of course), and isn't related to the one from Windows Mobile. At least that's what I'm hoping.