You seem to have described the general shape of a bell curve, but you go off the rails a bit with things like "There are more people who are, statistically, absolutely average."

The mean, sometimes also called the expected value, is defined as SUM(values) / N where N is the number of values. Using that definition and the definition of a Gaussian (which is what a bell curve is) you can prove that the mean falls precisely in the middle of the distribution: there are equal numbers above and below the mean. Since results of an IQ test are distributed pretty normally, the OP is correct: half of people have an IQ that is below average (and half have an IQ that is above average). There may in fact be no individual people who are exactly average. If the measurement is continuous then this is almost certain.

That result is extensible to any symmetric distribution (of which the Gaussian is one). In fact, the reason they're called symmetric distributions is because they're symmetric about the mean.

I teach statistics, by the way.