My phone does that too, it downloads apps so quick I sometimes wonder if it did anything at all. Since they're under "My Apps" then it means you downloaded it. To get them on your home screen, press and hold, select Shortcuts, select Applications, and then select the specific application you want to appear on your home page. A quick way of making sure they certainly do exist is clicking on the icon between the dialer and the browser, the one that shows you everything you have in a nice grid.
Does that help at all? Hahaha are the applications working at all?