A piece of ice with stone which is denser than water embedded inside, is kept in a vessel containing water. Size and mass of the stone is such that the stone - ice combination is floating on water. When ice melts what will happen to the level of water in the beaker?

Decreases! As the stone is embedded in the ice piece of ice, the effective density of the ice-stone system is more than that of ice alone. As a result more part of the ice gets inside water (if ice alone, only about 92% shall be inside water since its density is less than that of water).As the ice melts it needs less space inside water and the gap will be filled by flowing in some water from top. As a result the water level decreases!