from the pictures that is a standard design centrifugal pump. As said, it will not work without the bottom cover! It will also not work without the "shims". Those shims form the pump body, which is shaped like the numeral "9". If you look at the pump, you notice that the open center of the "shim" surrounds the impeller. The inlet screen is centered on the impeller. As the impeller rotates at high speed, the liquid is accelerated around the pump cavity. As the fluid at high speed hits the "tail of the number 9" shaped section of the pump body, it shoots through the opening and goes up the tube to the engine. You can see that if the pump is running backwards, it will not pump. If the liquid does not completely fill the pump cavity, it will not pump. This design pump is very efficient, and is used in all sorts of commercial, residential, and automotive applications.
I like the cotter pin idea! I have read several posts about the pump falling apart in the tank. That is some fine "field engineering" in action! If I ever have to pull mine, that will be a modification I perform.
Glad you got it back running!