1.) what energy transformation are taking place when a ball is dropped from 1.0 m, bounces and tries to 0.80 m, bounces again and rises to 0.64m? What is the efficiency of the energy transformations of ball during a bounce?

Answer 1

The various energy changes you need to cover are:
gravitational potential energy to kinetic energy
kinetic energy to elastic potential energy and to heat
elastic potential energy to kinetic energy and to heat
kinetic energy to gravitational potential energy
You could also mention kinetic energy and gravitational potential energy to heat due to air resistance.

The efficiency will be final total energy/initial total energy. Using E=mgh, by proportion it follows that :
Efficiency of 1st bounce = 0.80/1.00 = 0.8 (=80%)
Efficiency of 2nd bounce = 0.64/0.80 = 0.8 (=80%)
So the efficiency of the energy transformations of the ball during a bounce is 80%