Rich, pressure in a fluid acts in all directions (down, horizontally and, yes, upwards). You cannot have two separate columns that are in contact with one another. From the point of view of pressure and buoyancy, they are the same column. As I've already said, when you add more water to the top of the glass, you increase the pressure in the water at the bottom of the glass. Whatever the density of the new water.
A floating object displaces its own weight of water. In your example, the amount of water displaced by the ice cube would change when you add more water. This would imply that the ice cube had become heavier. This is clearly not the case. The only slight difference is as Binntho says, that the average density of the water has change. However, this would only mean that for each 1 cm of water you added, the ice cube would rise say 0.98 cm instead of 1 cm.
You should look up the buoyant force, hydrostatic pressure, communicating vases, Pascal's Principle and Archimedes' Principle.