I'm not convinced that a pump is the best way to oxygenate a pond. It works, but is not the best way. Better to have some oxygenating weed, such as elodea. That also makes a nice habitat for tadpoles and other water creatures. But don't add elodea now, do it in the Spring.
Ponds should be cleared out as infrequently as possible. The animals quite like mess, and they don't like distrubance. Some might like to overwinter in the mud, if the pond and the mud are both deep enough.
I'd be inclined to live with the present situation. If a lot of seed is floating on the surface, just skim it off. If, over time, so much seed has fallen into the pond that it completely silts up, then just trawl out a bucketfull of the mud. Don't think of taking it apart to clean it.