Skimmer set up

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I have the hose down from the overflow into a 10 gallon tank, then the powerhead to the Red Sea berlin classic skimmer. then there are two outlets. Then I have a wet dry filter.
Question: Do I take hoses from these two outlets then to the filter? Right now there is a lid on it that has a 1 1/4" input. I guess I can saw this off and drill two holes for these 3/8" hoses to fit into.
Am right in thinking that I cannot put these two hoses into a Tee and then to the 1 1/4" fitting, will there be too much back pressure.
Question: Does the powerhead before the skimmer need to be stronger, weaker, or the same gpm as the one after the bioballs returning to the tank?

 

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I have a rio 2500 so I think I have enough pump, the water flows from the tank to a 10 gallon tank where the rio 2500 sits and that is connected to the skimmer. I want to then take that and have the water go into the wet/dry through the bio balls. Then I have a CA 2200 that sends the water to a UV sterilizer, and then to the tank. The CA 2200 is rated at 650 gal/hr at the length of return I have.
Soooo, after all of that, can the two outlets be sent to the bio balls next? Right now the plate that is above the bioballs has a 1 1/4' pvc connection on it. I guess I would have to create anoter plate and affix fittings to accept the 5/8 hose or something. What are your thoughts?