With so much radio signalling occurring simultaneously (TV, Cellphone, Radio, etc.), how does our atmosphere keep them separated and avoid disruption?
I understand that different stations are given different frequencies, but waves are able to interfere with each other if they meet. If they do, they produce a completely new wave.

You are misunderstanding. When waves meet they typically superimpose and then pass through one another without generating a new wave. Generation of a new waveform requires nonlinearity at the point where they meet. This nonlinearity breaks superposition, resulting in the generation of new frequencies. For example, in light, a photographic plate can record a new frequency because it's response is nonlinear. A radio receiver can generate a new frequency because it has a diode or other nonlinear element. Without those nonlinear devices, there is no new wave or frequency.