As per your follow up post, the MCB would open, the main switch will stay put.
Correct.
Alas no. A MCB will only open on an overcurrent. This needs to be either a "fault current" or an "overload current".
See for an explanation:
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but power would remain on for the rest of the non-RCD circuits.
Correct. The big advantage here si you are not plunged into darkness should you get a trip. Historically they used to use a whole house RCD which would result in just this effect. What they found was it reduced electric shock injury, but then *caused* more tripping and falling injuries.
Depends. If the short is Live to Neutral then the MCB will open, but not the RCD. If it was live to earth then chances are one or both would open.
A simple multimeter test will be a good start. Stick it on its highest ohms range and check it looks like an open circuit when you measure between live and earth and neutral and earth. Stick it on its lowest ohms range and check it is about right for the power of the element. So a 3kW element at 240V should have a resistance of 240^2/3000 = 19.2 ohms. If it is significantly less then that is your problem. Note that it is possible that it may look ok on a multimeter, but then give poor readings at mains voltage - you would need more sophisticated test equipment to test this however.
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