I use the EV-240 (for a number of years now), which I believe is the same style as yours, just different aquarium gallons capacity.
I don’t have the piece with your hand on, and believe that’s the a waste collector in the event the skimmer cup fills up.
I’m using a Mag-12 pump on mine, but they also suggest using a Mag-18. I would guess yours would use the Mag-12 at the most, maybe a a Mag-9.5. Those are what AquaC recommends but you can use something along those lines. Mags uses some electricity. Will give off some heat as well, doesn’t affect my tank temperature though.
The skimmer doesn’t require an air input with the pump. The smaller gray/blue valve is the air input. I keep mine wide open. It will need rinsed out once in awhile because of salt buildup. The larger gray/red gate valve will control the water level in the skimmer. Basically you want the bubbles at the top of the darker bottom base when the pump is running. It will take a few days of breaking in and adjusting at the beginning.
The skimmer can be used in a sump or outside.
I have a hard copy manual of my skimmer (or an EV-180 I once had). I can look for it and can scan it into a PDF if it helps. They basically all work the same except the hang-on skimmers.