On the moon you would weigh much less than what you weigh on earth

Yes

Explanation:

Weight is a function of mass and gravity.

Since our mass is the same at anywhere in time, gravity is the determining factor. Gravity on earth is much larger than that of the moon.

The moon's gravity is only about 16.5% that of earth. We then expect the weight on moon to be just about 16.5% that on earth.

float.

archimedes' principle

denser than water sinks in water.

denser than mercury would sink in it