A piece of ice floats in a glass of water, in which a pellet is frozen. Will the water level in the glass change if all the ice melts?

Yes, it will change.
According to Archimedes’ law, water displaced by a piece of ice has a weight equal to the weight of ice and pellets together. When the ice melts, it turns into water equal to the volume of water it displaces. And the pellet has a density greater than that of water, and to keep it afloat, water with a larger volume was displaced than the pellet will occupy in the water after the ice has melted. This means that the water level will go down.