Is there a shorcut to maximize any window, especially an IE window?

Yes.

Alt+spacebar opens up the control-menu box of any parent window, then you can choose the appropriate shortcut letter (x for maximize, etc.).

For any child window, Alt+hyphen opens up the control-menu box of the child window.

Remember back in the days of Windows 2.0 and Windows 3.1? The control-menu boxes of the child and parent windows had a little "line" graphic in them... a long line for the parent windows and a short line for the child windows. These were actually mnemonics for space and hyphen.