For most devices the voltage and current ratings are "This Device Will Operate Properly and Safely As Long As You Do Not Exceed This Value."
A 40 amp contactor can open/close and turn on 0-40 amps. You could use it to switch 1/2 an amp, if you wanted. Hypothetically, at 40.01 amps you are exceeding the safe operating area for that contactor and at risk of damaging it.
In the example of the combination of contactor and receptacle, the receptacle 30 amp rating limits the associated circuit and you should not exceed 30 amps.
Some devices the voltage and current ratings is what they require to operate properly. One example is a 100 watt light bulb. It is telling you it will draw 100 watts of power. Therefore the circuit and it's associated components should be rated for 120 VAC @ ~1.0 amp.
Ok I understand better now. So does it mean that I can use 16 amp circuit breakers instead of the 15 amp as per the plan ? Because I found these and am not sure if I can use it.
As for the emergency switch, do I need a normally open one ?