You when you engage reverse you should immediately hear a short beep to let you know the system is working, you shouldn't hear anything else until you get close to an object when you will hear the beeps getting more frequent right up to a continuous tone when you have about a foot to go before impact!
Unfortunately the sensors are prone to failure (just had 2 of mine replaced). What will happen if you have a fault somewhere is that the first time you engage reverse you will hear a longer tone and then nothing else. This is to tell you that it's not working. This will happen the first time you engage reverse each time the ignition is switched on.
If you turn on the ignition, but not the engine, put it in reverse and put your ear at each sensor you should hear a quiet buzzing sort of sound. A duff sensor won't buzz.
I got mine replaced under my RAC warranty so not sure of cost, if you've just bought it I would take it back and see about a partial refund, the fault on mine started out as intermittent so I would be surprised if the seller didn't know about this.
The switches on the door are to do with deactivating the alarm sensors.
Best of luck and happy New Year, apologies if this is a bit of a ramble, I'm still in recovery mode!