Where does Windows store icon positions?

They are located in the registry under HKCU\Software\Microsoft\Windows\Shell\Bags\1\Desktop.

The key that should interest you is the ItemPosXXXxXXX(where XXX is your resolution).

enter image description here

The relevant values are Mode, LogicalViewMode, IconSize.

You can combine them as shown in the table:

Style       Mode    LogicalViewMode  IconSize
X-Lg Icons  5       3                0x100
Lg Icons    5       3                0x60
Med Icons   5       3                0x30
Sm Icons    2       3                0x10
List        3       3                0x10
Details     4       1                0x10
Tiles       6       2                0x30

Update

Fortunately found an article that can help you. See: Windows Shellbag Forensics.