Welcome to the forum.
Your pump is probably fine, more of a design issue. With a top flow filter, if you get too much flow, it will go over the top. Air space is not necessarily bad if the water is distributed evenly so it can trickle/spray down throughout the media.
One version of a bottom flow filter, think L-shaped PVC manifold pipe, water enters at top but exits at the bottom of the pipe, flowing upward, filling the container, until it enters the overflow which returns back to the pond. I use this type and have lava rock in bags as the media. Nice feature is it helps solids to settle out at the bottom of the barrel as the water velocity decreases which can be removed easily if you have a bottom drain.
Unfortunately, a bio filter of this type will do little to eliminate the green water algae. Setting up the return as part of or a completely separate bog filter is what you need as the most trouble free long term solution without using UV.