Why does installing an app take so long? What exactly happens when you install an app from a .dmg image. My understanding was that it changes the inode and makes it executable (the specific application was GNU Scheme). But that can't be it since it takes about ~1m.
DMG is a disk image file format.

Disk image files behave like a physical disk. In so doing, the operating system interprets them in the same way as if you had just inserted a CD-ROM, USB drive, etc into the computer. 

Therefore, how long an application takes to install depends almost entirely on the application itself (e.g. It's size, whether it needs an installer, etc) and other factors such as the speed of your drive.

For more info on DMG files you may want to read my answer here.