That is, there are no forces of attraction or of repulsion between them. Thus there is a wide range of kinetic energies in any gas. However, the average kinetic energy for any gas is the same at a given temperature. The average kinetic energy for the particles in a gas is proportional to the absolute temperature of the gas. This explains why gases rapidly fill their containers.
Brownian motion is also a consequence of their rapid movement.
Three is a bit more subtle, and we won't worry about it. From this postulate we expect a distribution of velocities. Notice also that the energy increases with the square of the velocity.