For the switch you could use a reed switch, a hall sensor or a electromechnical switch. I might be an idea to sense the hatch instead of the door.
It takes a certain amount of energy to heat a body. For a homogeneous body it s mass*specific heat capacity. In SI units Water has a specific heat capacity of 4,2 kJ/kg/K meaning it takes 4,2kJ of energy to heat 1kg (or 1 liter) of water 1K (or 1C). Since 1j = 1Ws heating power directly corresponds to heating rate. A heater with a power of 4,2kW will heat 1kg of water 1K in 1s. Or a 1kW will rise the temperature in 1 kg with 0,238K each second or 1K in 4,2s.
A resistor converts electrical energy to heat with 100% efficiency. Electrical power is P=U*I. Combining this with Ohms law yields P=U^2/R or R=P/U^2.
It is possible to vary the rpm of the motor to alter the pressure and the flow rate in the pump. A PM DC motor can be regulated by varying the voltage or using PWM. A AC motor driving a pump must be regulated using a frequency converter.
Solenoid valves for these types of applications are quite common an easily available. These are on/off valves with no flow regulation.
Dishwashers and washing machines and similar appliances are most commonly modeled using state machines.