Do placed units increase in damage when you level up the ability? [duplicate]

The abilities will level up with you.

After placing a Teemo Mushroom, Shaco box, Caitlyn trap, Nidalee trap, or any other placeable unit, when you level up the respective skill, the placed unit will level up as well and receive an increase in attributes such as damage.

Note: Heimy's placed turret's health will not increase if you level up the skill

Also, the placed units are basically referencing your skill in its current state, so buying items will have an affect on already placed units, same as levelling them would.