Hi Simone ,
i'll only answer the first query this time.................
now u see that initially when the mass m was lowered slowly to its equilirium position then it extended the spring by an amount d . now in the question it must be mentioned that whether in the second situation they want the maximum extension of the spring or final extension n the spring . ......
when we let the mass m fall freely then it it gains up some velocity and goes further away from its equilibrium position and stretches the spring more than d ..then it comes back again towards the equilibrium position and eventually settles down to the equilibrium position after some oscillations ..... so we can say that finally the extension in the pring will be equal to d only .......