If your shortcuts aren't working, something is interfering with them. Instead of Alt+Tab, try Window-Key+Tab to do the Flip 3D application switch. Does that work? If not, try plugging in another keyboard. If it still doesn't work, then you have a driver or program that is interfering with your keyboard.
Now, as to Steam, it shouldn't need to run in compatability mode. If you right-click on the Steam shortcut and go to properties, check the Compatability tab, and also under the button that says "Show settings for all users." You may get a UAC prompt, but that is okay. Make sure no compatabiity modes are on. If it still triggers compatability modes, then uninstall Steam and re-install it. Something may have gotten done oddly upon installation. You can uninstall Steam and reinstall it without having it remove your game-file cache, so no need to re-download and reinstall your games.
As far as UAC popping up each time when you run the old version of Steam, that is because it wants to update itself, and needs admin access to run the installer or modify its files. This is fine, and expected.
-Kurtis Whittington- Microsoft Windows Client Team