How does the male gamete penetrate the egg cell? How does the female gamete protect itself from the entrance of more gametes after the entrance of the first sperm cell?

The sperm cell that reaches the egg cell triggers the acrosome reaction, a process in which hydrolytic enzymes of the acrosome are released on the external surface of the zona pellucida (the protective layer that surrounds the egg cell). A portion of this layer is digested by the acrosomal enzymes permitting the sperm cell to reach the plasma membrane of the egg cell carrying out fecundation.

At the moment that the sperm cell makes contact with the egg cell membrane a chemical alteration of this membrane happens. Enzymes secreted by exocytosis (cortical reaction) make the zona pellucida unable to bind to other sperm cells (zonal reaction) and other male gametes cannot enter the egg cell.