So any check valves much above the pump should be removed. Any bleeder valves should be removed.Pressure tank is a fiberglass Wellmate with bladder.
If the Wellmate pressure tank with a bladder fails, you would want to go to a similar looking and working tank with a diaphragm rather than a bladder. The diaphragms tend to be longer lived.
Pumps would often have a check valve built in. Even if there is a check valve in the pump, it is OK to put one a little above the pump.Myers pump that had mud covering over half of the intake. I thought there was a check valve above it but could be wrong. I didn't look that close at it.
Maybe you could get the well cleaned out. The fast way is with a big engine-driven compressor blowing air. Maybe 200 cfm give or take. The debris shoots up like a geyser. The slower way uses a much smaller (maybe 5 or so cfm) compressor and an air lift pump (usually homemade). An air lift pump needs some proportion of the casing to be filled with water.