Where to start?

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How is it possible to amplify the input signal, divide it and compare the original signal, when I assume the incoming signal has changed by the time this processing has taken place? Does this all happen instantaneously, or is there a record of the incoming signal held momentarily somewhere so that it can be compared after the processing has taken place?

Negative feedback does nothing to correct the incoming signal then, only corrects the amplified signal.
 
Indeed, it only corrects the amplified signal and it only works well when the input signal varies slowly compared to the speed of the amplifier (in jargon, has a bandwidth small compared to the loop bandwidth and a rate of change small compared to the slew rate limit). Fortunately, audio signals normally meet that condition. If you were to build a 10 GHz RF amplifier, it would be very difficult to make the circuit so fast that negative feedback gave any benefit at all.
 
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