If defined traditionally (from the Greek), it's the literal truth.

http://www.etymonline.com/index.php?term=idiot&allowed_in_fr...

Depends on the distribution. And which average.

IQ is distributed normally.

That's begging the question.

what do you mean?

The definition of IQ says that it assumes a normal distribution, with half either side of the mean. To use the definition of IQ as a justification for the statement "half of all people have less than average intelligence" assumes that the distribution of intelligence matches the distribution of IQ.