It is a solution. For chocolate syrup and milk to be a mixture you would have to be able to mix it together and then separate them, making chocolate syrup and milk again. You can't do this. When you mix them together it makes a completely new substance that cannot be changed back to the things that you orignally had. Therefore it is not a mixture.
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It mixes by gently stirring the powder into the milk before gently shaking it. it depends on the consistency and thickness of the milk used.
Chocolate syrup is denser and weighs more than milk does, so it sinks to the bottom of the glass due to gravity.