Why is the calorimeter assembled by placing one cup inside the other?

If you are piling cups of the same size, then it will efficiently double the thickness of the isolating walls. Think of this as amplifying the thickness of the insulation to preserve the heat inside the cups from evading. When you measure the heat of the reaction, you want to arrest all of the heat from the reaction. A calorimeter does this by measure the alteration in temperature of the solution or gas round the reaction and then calculates the heat that was generate by using the specific heat of the liquid, typically water, or the gas.

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.