Your calculations are correct, but your subsequent questions need some explanation. I'll base my answer on standard Round Earth physics. FEers can give their own explanation if they want.

You need to remember that mass and weight are not the same. Mass is something that is inherent to an object. Weight is a force, which depends on both mass and acceleration, with F=ma (Newton's second law).

On the surface of the earth, where the gravitational acceleration is about 9.8m/s^{2} the "weight" of an object is the same as its mass, i.e. a person with a mass of 100 kg will weigh 100 kg. However, on the moon, where the gravitational acceleration is 1.6 m/s^{2} they would weigh only 16.3 kg. To avoid the confusion of having kg (or lb) used for both mass and force, in the SI metric system kg is the unit of mass, but force is measured in Newtons (N). 1 N is the force needed to accelerate 1 kg with 1 m/s^{2}. Hence a person with a mass of 100 kg will have a weight of 9800 N on earth, but 1600 N on the moon.

Because the imperial system does not distinguish between mass and weight, I felt I had to give the above explanation in metric units. If you do want talk in imperial units, multiply every instance of kg in the above paragraph by 0.454 and multiply every m by 0.305 to convert to ft.

Now for your questions.

1. No, the person's density does not change, because neither their mass nor their volume changes.

2. As explained above, a change in weight is not the same as a change in mass. In this case it is simply the acceleration that changes the weight, while the mass stays constant.

3. When going at constant speed there is no acceleration. Hence on earth the scale will read 100. On the moon the same scale will only read 16.3

Trivial fact: there used to be a minor difference (about 1/63000) between the British and US inch. That was finally sorted out when both countries agreed that one inch is exactly 25.4 mm. In other words, they agreed on a metric definition of the inch!