Where did Alt+F4 come from? And why aren't there any other similar Alt keys? Why F4? I'm sure that is something that has left a lot of people scratching their heads.

I still don't know if it was influenced by some other earlier program, but ALT+F4 first appeared in Windows 2 and then OS/2 1.1.

Windows 1.x did not implement ALT+F4. Around the time of Windows 2 and OS/2 1.1 there appeared to be a push to increase keyboard accessibility, which also brought the addition of custom menu hot keys. I'd be mildly surprised if IBM didn't have something to do with this.

Windows 2 (and OS/2 1.1) added the following keys for window manipulation:

ALT+F4 - Close
ALT+F5 - Restore
ALT+F7 - Move
ALT+F8 - Size
ALT+F9 - Minimize
ALT+F10 - Maximize

And for child windows in a multiple document interface application:
CTRL+F4 - Close
CTRL+F5 - Restore
CTRL+F6 - Next
CTRL+F7 - Move
CTRL+F8 - Size
CTRL+F9 - Minimize
CTRL+F10 - Maximize

Logically ALT+F6 would be "Next" for main windows, but neither Windows or OS/2 appear to use that. CTRL+F6 is used by the OS/2 1.1 file manager for moving to the next child folder window. ALT+F6 is used by MS-Word 1.1 for Windows to move to the next child document window.

Interestingly, many recent MDI applications for Windows still use CTRL+F6 to switch between child windows.

Windows 2.x did not include any multiple document interface applications, but Word and Excel for Windows 2 do use the CTRL+Fx keys to control child document windows.

Windows 3.0 removed all of these key combinations except for ALT+F4. Presumably to remove visual clutter in the system menu, and free up key combinations for other applications.