It does fall to the ground. There’s more air closer to the surface of the earth. Think about a pile of sand. The closer you are to the ground, the more sand (air) there is.
For your second question: Fluids exert pressure. Pressures create force (buoyant force) on surface of objects. If the force is greater than the weight of the object then the object will float or rise to the top of the fluid.
The denser the fluid, the greater the pressure. The lighter the object, the lesser the weight.
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