I tried installing the editor into the ICW folder, but it didn't recognize anything. Also, it requires the bink32.dll or whatever it's called, and the other .dll's from the "corruption" folder.
I've also heard that you can install the map editor in the mod's folder rather than moving the mod into FoC's folder, but I've not tested this approach.
Not if you only intend to play the mod, since it would mean just launching the game launches the mod, but it would interfere with other mods and prevent you from playing the base game.
The map editor typically reads from the default data folder, so if you want to use the map editor with ICW, you would need to copy everything from Imperial_Civil_War/Data and paste it into Forces of Corruption/Data. It's easiest to make a backup of the original FoC data folder if you do this, too.