The only reason a prefilter will cause a pump to burn out is if the filter stops the water flow to the pump. If you clean it each week,, as suggested by Aiken, it will be fine.
If you post pictures of the remaining shrimp, and a picture of the entire aquarium, we might be able to identify an issue.
What fish are in the tank with the shrimp?
How long has the tank been set up for?
What are the tank dimensions (length x width x height)?
How often do you feed the fish and shrimp?
How often do you do water changes and how much do you change?
Do you gravel clean the substrate when you do a water change?
Do you dechlorinate the new water before adding it to the tank?
How often and how do you clean the filter?
How long has the filter been running on the tank for?
Do you ever replace the filter media?
Many apologies for the late responses. I had bad internet connection today, and I am neurodivergent, so sometimes I lose focus.
The aquarium is a 10 gallon. 20 x 10 x 12. Was set up about a couple days before Christmas with sand and a coconut shell with java fern on top. After two months, a nerite snail and another plant I don't know the name of were added. That was last month. About two or three weeks ago, I ordered six pygmy corydoras and ten red cherry shrimp online. I have fed the fish and shrimp usually once a day, or once every other day. Today I will start to feed once or twice a day because I now know that I am not overfeeding them.
Did my first water change of a gallon on Saturday. My gravel vac doesn't work too well because the tank is on the ground, but the sand was coming up clear when I tried.
I did find a shrimp today that was missing. I found my first exoskeleton on a piece of hornsworth (along with another nerite snail, two moss balls, and another small potted plant I don't know the name of were bought within the last week or so), so I'm guessing he was hiding so he could molt in peace. I left the exoskeleton on the branch so that he could eat the shell. I only found four dead shrimp, so there may still be two more alive in the tank.
I always dechlorinate with the api tapwater conditioner. I try to put one droplette, but it usually ends up being almost 5 mL in a gallon of water that I add to the tank. AqAdvisor says only a 13% water change is necessary, so I am doing a gallon for now.
Filter has been running since the tank was set up, with the media having never been changed yet.
I currently have a piece of drift wood that has been soaking for about a week in a bucket.
Any advice or suggestions would be greatly appreciated, Colin. I see you are another person that helps people as well. Thanks!