If your well pump is cycling, that's your problem that's causing the low water pressure that's causing your other problems. You need to address that, and it should solve the other problems.
Pump cycling could be for any number of reasons.
First thing to check is the pressure tank.
Turn the pump off, drain the water pressure off, and check the air valve on the pressure tank with a tire gauge. It should be two psi below your pump cut-on pressure (18 for 20 psi cut-on? 28 for 30 psi?). Your pump should be 20-40, 30-50 cut-on/cut-off psi, etc.
If it's too low, air it up with a bicycle pump or portable air tank or compressor.
If it doesn't hold that pressure, the bladder is shot and you need a new pressure tank.
If THAT isn't it, come back and we'll go to Plan B.