1) "after every fall, the kinetic energy of the ball decreases by a factor of K". So if K > 1, that means the energy becomes negative? E_2 = E_1 - E_1*K might be interpreted to be what you mean when you say something decreases by some factor.
2) "Your task is to determine the maximal distance from the point of throwing that the ball can fly." If the ball is pitched straight up, it will fly some maximal distance from the point of throwing before it reaches the ground again. You should probably exactly what you mean.