The ideal gas is a 'model' of how an actual gas behaves. It is still used because it agrees with many different types of experiments on gasses, but its limitations are also recognised.
The initial assumptions are that molecules are represented by perfect and elastic spheres of infinitesimal size, these particles travel in straight lines and strike the walls of any vessel in which they are contained. By being elastic means should they collide with one another no energy is lost, i.e. no energy is retained within a particle so that the total kinetic energy after collision is the same as before collision, but their direction and hence momentum changes.
On collision ideal gas particles impart momentum to any wall thus producing pressure. The collision with a wall is elastic so no energy is lost. The incident and reflected angles are the same. To calculate the pressure ($p$) we do not need particle to particle collisions and all molecules can travel at the same speed then
$$p=\frac{2\cdot \mathrm{kinetic\; energy}}{3\cdot V}$$
where $V$ is volume. Even if there were collisions this would not affect the pressure as this is caused by collisions with the walls.
As kinetic energies are additive so are pressures, this means that the pressure of mixtures is the same as that of each gas taken separately which is Dalton's Law. If the volume changes it does so in inverse to the pressure which is Boyle's law.
If two gasses at different temperature are allowed to mix, say by removing a partition between them, they will diffuse into one another and at the same time the temperature will eventually become uniform throughout the gas. This can only happen if collisions between particles occur, so this is an essential assumption of the ideal gas model, unrealistic though it may seem for particles of an infinitesimal size. Once the absolute temperature is introduced the kinetic energy can be shown to be $3RT/2$ which produces the ideal gas law via the previous equation.