Is there not a way to adjust the water level in the skimmer?
From all your pictures it looks like your just not getting much air into the chamber and all water. The more air the pump draws, the less water will be drawn into the chamber.
It looks like your having an air problem. Not enough air means way too much water and it will overflow like you are having.
For example my skimmer is an in sump style but they work the same. Mine has an exhaust tube that is used to adjust the level in the skimmer but also if the air tube gets blocked even if the skimmer was adjusted properly, the cup will start overflowing with just water.
Make sure your air tube is not kinked or blocked in any way.