Can Implant Suggestion force stationary monsters (either Yellow bordered monsters or monsters such as Liogor or the Dunwhich Horror) to move? Or does it have no effect on Yellow monsters and treats others as if it were a normal movement - and if so then what about Aquatic monsters?

You may cast and exhaust while in Arkham to choose one monster in your location and have it move either in the direction of the white or black arrow in that location.

Seems clear to me. The monster forgoes its regular movement type and simply moves one space towards white or black. Or rather, you are moving the monster one space away. "Location" here was probably a misprint too: I'm sure you can cast this in a street.