The Space Shuttle, so far, has killed fourteen people, merely trying to
attain an orbit about two hundred fifty miles above the Earth.

How is it then, that a third of a century ago, with less computing power
in the entire rocket than in a present day twenty dollar Wal-Mart watch,
NASA claims to have gone 100,000% farther, six different times
between 1969 and 1972, landing on another celestial body and then
returning, without ever killing anyone?

The Apollo program killed at least three that we know of.  Both the
Apollo and Space Shuttle "accidents" involved low tech ironically.
All the deaths in retrospect were very avoidable.  Oxygen being used
where it shouldn't have been.  Frozen "rubber" O-rings.  Glued tiles?
I also believe the people involved in the Apollo program were more
competent, individually, and as a group.

How could they have powered air conditioning in two hundred fifty
degree heat for three days with batteries?

Most of the cooling was done by the material of the suit.  As someone
has already pointed out on a similar topic in these groups recently,
the heat on the Moon is radiative not conductive.  All you need to do
is reflect the heat.  The backpacks that the astronauts wore was to
moderate the temperatures and humidity produced by their own bodies.

Why is the "second round" of "returning" to the moon estimated to be
no earlier than half a century after the first?

(Would there be a fifty-year span between the first and second
trips across the Atlantic in an airplane?)

Probably because we've been going there secretly.  If we did find
evidence of former intelligent life on the Moon the pressure to
investigate and exploit any potential technology would have been
imperative for national security.  We may very well have bases on the
Moon right now.  And if we do, we probably have been to Mars as well.
Hard to believe, but far from impossible.

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