How to install Mac OS X from Windows on MacBook Air? I have OS backup .dmg installation file. The problem is I have Windows 7 on my MacBook Air, and I do not have access to OS X to use Disk Utility to burn/restore the OS X image.

Is it possible to burn/restore .dmg file on usb stick from Windows?
You dont need accessing it from windows. 

Boot the computer holding the [option] key and choose the OSX recovery. Inside it there you'll have a very basic osx with its own Disk Utility to restore your DMG image to another USB.