Here are some explaination to your questions:
Some of the Apollo video shows the American flag fluttering. How can the flag flutter when there is no wind on the airless Moon?
This I find to be one of the more ridiculous observations. It is readily apparent that all the video showing a fluttering flag is one in which an astronaut is grasping the flagpole. He is obviously twisting or jostling the pole, which is making the flag move. In fact, in some video the motion of the flag is unlike anything we would see on Earth. In an atmosphere the motion of the flag would quickly dampen out due to air resistance. In some of the Apollo video we see the twisting motion of the pole resulting in a violent flapping motion in the flag with little dampening effect.
I've heard many hoax advocates claim that some of the Apollo photos show a fluttering flag. (How one can see a flag flutter in a still photograph is a mystery to me!) I can only guess that ripples and wrinkles in the flags are being perceived as wave motion. The flags where attached vertically at the pole and horizontally from a rod across the top. On some flights the astronauts did not fully extend the horizontal rod, so the flags had ripples in them. There is much video footage in which these rippled flags can be seen and, in all cases, they are motionless
The Lunar Module weighed about 17 tons, yet the astronauts' feet seem to have made a deeper impression in the lunar dust.
The hoax advocates often quote the weight of the Lunar Module as 16 to 18 tons (weights varied mission to mission). This was the LM's Earth weight when fully fueled and included about 9 tons of descent stage propellant. By the time the LM reached the surface, its weight in lunar gravity was only about 2,700 lbs. With four 37-inch diameter footpads, the load on the surface was about 90 lbs/ft2. Neil Armstrong's fully suited weight on the Moon was 58 lbs. His boots covered an area of about one square foot, giving a load of 58 lbs/ft2. In Armstrong's own words "the LM footpads are only depressed in the surface about 1 or 2 inches". On the other hand, the footprints of the astronauts were depressed only a fraction of an inch, although people often exaggerate their depth.
The black sky should be full of stars, yet none are visible in any of the Apollo photographs.
This claim is one I hear frequently, and is one of the easiest to refute. The answer is very simple: they are too faint. The Apollo photos are of brightly lit objects on the surface of the Moon, for which fast exposure settings were required. The fast exposures simply did not allow enough starlight into the camera to record an image on the film. For the same reason, images of the Earth taken from orbit also lack stars. The stars are there; they just don't appear in the pictures. The hoax advocates often argue that stars should be visible, and some of their claims are valid, however they fail to recognize the difference between "seeing" stars and "photographing" stars. The astronauts could have recorded star images in their photos by increasing exposures, but they were not there to take star pictures. The purpose of the photos was to record the astronauts' activities on the surface of the Moon.
Bill Kaysing claims that NASA has perpetrated the lie that stars cannot be seen in space to validate the lack of stars in the Apollo photos. This assertion is utterly ridiculous; in fact, NASA has released many photos in which stars are visible. Common among these are long-exposure nighttime photographs of aurora taken by space shuttle astronauts.
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