I just downloaded IE7 the other day. So far, it works well enough, but since I'm a Firefox user, I haven't played much with IE7. Just yesterday, I downloaded Firefox 2.0. It has a spell checker built in and a few other changes that I haven't paid much attention to yet. It's working nicely as well.

As far as your missing icon. You could try right clicking the desktop, then properties, then the desktop tab. Finally, click the Customize Desktop button. In there, you should see an option to show the IE shortcut on the desktop. I have my computer set up for classic view, so your steps might be different.