No, the Pondmaster 2000 cannot be used with a skimmer. Both the skimmer and filter have to connect to the pump's intake. You could add a tee connector to connect both devices but one or both wouldn't get much suction. You can add valves to try and balance it out if you want.

You could just toss out the filter. It really is a very poor filter. Won't really do anything and is a pain to clean. You can remove more stuff by scooping around the bottom with a net and that's way easier than cleaning that filter. Your call.

Having a pump on the bottom can lead to unwanted clogs. The big problem is if the output from the pump goes outside the pond, like to a filter, waterfall, whatever. Should something outside the pond leak the pump, being on the bottom, will drain the pond. Happen to a pond that I sold. New owners hired a "pond expert" who moved the pump to the bottom, sold the new owners a crappy $500 filter. Week later the filter fell apart, pump drained the pond, killed all the fish.

If the pump water stays in the pond there's no danger.

The reason people say to put the pump on the bottom is to mix the water in the pond. As water moves near the surface gas exchange takes place, O2 enters the water and CO2 and other bad gases exit the water. But, the very same thing can be accomplished by having the pump near the surface and directing pump output toward the bottom. Moving water is moving water.