You say they spent a relatively short amount of time in space. Do you know the distance from earth to the moon? How fast did the modules travel?
They did. The entire Apollo 11 mission duration was just over 195 hours - or a little over 8 days - less than 24 of which were spent
on the moon. And yes, I know the distance from the earth to the moon - down to the millimeter, actually, courtesy of the retroreflectors left up there.
If the radiation they received wasn't such a big deal, why is NASA still trying to come up with ways today to protect astronauts from it during future possible trips to the moon and mars?
It's not that the radiation they received isn't a big deal: most astronauts in the Apollo program developed a number of health ailments as a result of their exposure. I simply said that the dose of radiation they received
in the few days they spent in space was almost 25% of the dose allowed in an entire year for people who work in environments where radiation exposure is a danger.
As for why NASA is trying to come up with better ways to protect astronauts, it should be be obvious: a mission to send humans to Mars would require a
much, much, much longer transit time than a mission to send humans to the moon. What good is putting live humans on a spaceship to Mars if what arrives is a blob of dead, highly irradiated flesh? Even if our goal is to only go back to the moon, doesn't it make sense to research better radiation shielding options anyways? If nothing else, such options would have numerous applications here on earth.
Still, a small amount of thrust from the rocket should've displaced some amount of dust on the moon's surface or at least left a mark, but nothing is shown on the pictures.
There was a mark made - the engine's thrust eroded the hard lunar surface, despite the fact that the engine had been throttled way way down; that "crater" is visible in at least two pictures.
According to the article I read, a 1966 National Geographic edition supposedly contained information about MIT scientists achieving the same thing. It also mentions the New York Times stating that the Russians had been doing the same thing since 1963.
Right. It's possible to do laser ranging even without a retroreflector, nobody aruged otherwise. It's just exceedingly more difficult, but not impossible. That's why the Russians left retroreflectors and that's why we left retroreflectors: to make laser ranging easier. The Russian retroreflectors are on the landing craft of their Lunokhod 1 and 2 missions. Small retroreflector units from Apollo 11 were left on the surface by the Americans. The large retroreflector arrays from Apollo 14 and 15 were also carefully installed on the surface by Americans.
These are
facts. The presence of those devices is
proven and can be verified - all it takes is a laser and somewhat affordable detection equipment and you too can do laser ranging. That the retroreflector arrays left by Apollo 11, 14 and 15 were carefully installed by humans is obvious to anyone who sees pictures of the arrays from the moon, as well as the pictures taken from spacecraft orbiting the moon.
Reality according to whom?
Reality is reality and it's not according to any one particular person.
Where are all of these independent recordings? I got this quote from the article:
As Reuters reported on August 15, 2006, “The U.S. government has misplaced the original recording of the first moon landing, including astronaut Neil Armstrong’s famous ‘one small step for man, one giant leap for mankind’ … Armstrong’s famous moonwalk, seen by millions of viewers on July 20, 1969, is among transmissions that NASA has failed to turn up in a year of searching, spokesman Grey Hautaluoma said. ‘We haven’t seen them for quite a while. We’ve been looking for over a year, and they haven’t turned up,’ Hautaluoma said … In all, some 700 boxes of transmissions from the Apollo lunar missions are missing.”
So they misplaced the "original" recording (I use the term original loosely here). That sucks and they should be flogged, but so what? Large parts of those transmissions, including the seminal "small step" were seen by millions of people, live, on television and archived footage exists. It's even on youtube!
Of course I know how the moon reflects light from the sun to lighten the sky at nighttime. Are you saying the earth would in fact reflect the same light from the sun onto the moon? We're taking of different surfaces here.
I am saying that the earth reflects light from the sun onto the moon, similarly to how the moon reflects light from the sun onto the earth. The fact that the earth shines so brightly and prominently in pictures from the moon should be proof of just how much light it is reflecting.
Also, wouldn't the light reflected from earth be somewhat 'overshadowed' by the sun's light, as it is way brighter?
That's not how light works...

I'll try to keep researching the issue as, at least to me, it is very interesting.
You may want to start from
http://en.wikipedia.org/wiki/Apollo_Moon_landing_hoax_conspiracy_theories where all of the questions you've posed so far are already answered, and citations to original sources can be found.