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Google takes the total cost for all the clicks and divides by the number of clicks to get the average cost per click. Simple math.
Yes you'll never see an actual breakdown of the clicks - always just an average.
Quite correct. And just to add a bit more detail, each click is quite likely to cost a different amount - which is dependent on the competitive landscape at the moment the search takes place.
The actual cost per click will always be less than (or equal to) the Maximum CPC set by the advertiser for the Ad Group (or per individual keyword if the advertiser has set things up that way).
Yes with a caveat. CPC price used to be much more in line with actual click thru rates. Once Google added the quality score factor of the CPC algorithm, click thru rate has become (in the majority of the cases) less of factor in the how the price is determined.