Ice crystals trap air as they form and the water freezes. This can make ice cubes appear cloudy. Minerals in the water and soap residue in the tray can cause ice cubes to stick to the tray. Try cleaning the ice cube trays with vinegar. Wash and rinse thoroughly before refilling with water.
Ice cubes freeze from the outside in. Ice is formed from pure water (hydrogen and oxygen) therefore the minerals such as calcium and magnesium normally found in the water sometimes end up as visible particulates in the core of the ice cube. The white particles are not toxic.