Turn over means to rotate it(be it an objet or being). Also it depends on the context of the sentence. In a business vontext it cam ewually mean profit/loss. eg. The turn over from my investment was very low. Turn around is a 360 horizontal/vertical turn where you look from side to side and backwards. eg. You will notice the change if you turn around.

We don't usually say "turn from up to down". "Turn around" and "turn over" are rotations that are relative to the orientations "vertical" (in the direction of up and down) and "horizontal" (in any direction that is perpendicular to vertical). You understand "turn over" correctly: moving something so that the side that was facing up is now facing down and the side that was facing down is now facing up. In mathematical language we can say rotate about a horizontal axis. You also understand "turn around" correctly: it means to turn so that the side that was facing to the left is now facing to the right, or the side that was facing to the front is now facing to the back. In mathematical language we can say rotate about the vertical axis. In ordinary speech "turn around" can mean either turn to face the opposite direction (turn 180° on the vertical axis) or it can mean to turn in a complete circle (turn 360° on the vertical axis). However, "turn over" almost always means to turn the top side to face down (turn 180° on the horizontal axis). Another usage of "turn over" is when talking the replacement of members of a group over time, such as employees in a business, members of a club, or items for sale in a store. Another usage of "turn around" is when taking about reversing direction when moving.

Up to down isn't typical English. Turn over means to rotate it, usually 180 degrees horizontally. Turn around is vertically. Imagine a person turning around, which is a common way of turning back. Hope that helps.