The impact velocity is 14.14 m s-1, derived from square root of two g h. Total kinetic energy equals 150 J, which divided by 3000 N resistive force gives a sand depression depth of 0.05 m.
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For rotational balance, effort times effort arm equals load times load arm. Since the adult has twice the weight of the child, the child must sit at twice the distance from the fulcrum compared to the adult.
The required energy depends on flag mass, gravitational acceleration and pole height. Raising it slowly or quickly does not change the work done. Doubling the lifting speed halves the time, doubling the required power.
Statements (iii) and (iv) are correct. At the highest peak, vertical velocity momentarily becomes zero making kinetic energy zero, while the entire initial mechanical energy turns into maximum gravitational potential energy at that height.