I made a water garden in a small Vietnamese water bowl - need advice!

The interior of the round ceramic water bowl is 25 inches across. It's 12 inches deep in the middle, but there is a little hole about 3 inches down from the top, so the actual capacity of the bowl is 9 inches at its deepest point, gently sloping up. It's glazed celadon green inside and out.

The nursery where I purchased it also sold me a little pump, 35 gallons per hour capacity. I got some oxygenating plants - something called hornwort (I think it is Ceratophyllum demersum) and parrot's feather (Myriophyllum aquaticum). They just float in the water. I set up the bowl outside my townhome in as sunny a spot as I have, ran an outdoor extension cord, and set up the pump. Apparently that little hole is made to run the electric cord through, but I can't figure out how to get the plug off the cord so currently the cord is up and over the side of the bowl. I put a chemical in the water to neutralize the chloramine. The whole thing looks very cute and I hope it attracts frogs.

Here's the problem. The hornwort died a couple of days later, and it fell apart in the bowl, and all those little needle-like leaves clogged the tiny pump. So I poured out the water and started over. I got some more hornwort. While I was at the garden center I picked up another plant that looks like a floating four-leaf clover (Marsilea mutica). Everything looks cuter than ever. I'm having to clean out the pump several times a day, though. This involves unplugging it at the source, pulling it out of the water, prying the tiny thing apart, and fishing out the tiny strands of dead hornwort leaves - kind of like miniature pine needles - from inside the pump. There has got to be a better way. Maybe a little cage to put the pump in? I'll look online.

Does anyone have any experience with water gardens in little bowls like this? The water gets quite warm in the sunny afternoon. I'd like to try fish or a miniature waterlily but I don't want to do that until I get the garden stabilized and the pump issue resolved.

What about hornwort? I read that it can die off like this when it is first moved from one place to another. Any tips on keeping it alive?

Maybe I should get a little skimmer to keep junk out of the water.