"NASA experts recently admitted that they currently do not have the capability of sending manned missions to the moon. So how could they have done it more than 30 years ago?" "...the computer onboard the Columbia had a capacity smaller than many of today's handheld calculators."
The problem is that when the Apollo program was terminated, NASA went for the Space Shuttle, which is fundamentally a low-earth-orbit vehicle (and a pretty shit one at that). Since all their resources were tied up in the shuttle, including launch pad design etc, it was no longer possible to manufacture and launch the giant rockets necessary for sending high-tonnage payloads to the moon and beyond.
Fortunately, the Space Shuttle program is now on it's way to being scrapped, and they're bringing back the old rocket design (rather than a modified plane stuck on it's end), so manned lunar exploration will be possible once more.
The photos are too good, the astronauts appear to "be well lit on all sides, regardless of where the sunlight is coming from, as if there were some artificial light source".
"Even when everything else is in shadow, the American flag and the words "United States" are always well lit."
Lunar regolith scatters and reflects light, much like the ground does on Earth, thus objects which are elevated (flags, astronauts, lunar module) are illuminated by the reflected light, wheras areas closer to the ground (shadows under rocks, depressions etc) aren't exposed nearly as much due to the smaller angle between them and the rest of the terrain. The surface is also uneven, so light comes from many angles.
Absence of stars in photos of lunar sky.
That's a very simple matter of exposure times. It's impossible to show both the very bright lunar surface and the very dim stars in the same photo without either having the lunar surface overexposed to the point of being pure white, or having the stars underexposed to the point of invisibility.