First, there is electromagnetic radiation. This is thought of as travelling as 'waves' through space. Light, radio waves, X-rays, infrared and ultraviolet rays are all kinds of electromagnetic radiation. This is what astronomers are usually talking about when they refer to 'radiation'. Gamma rays, which are also produced by nuclear processes, can be thought of either as 'ionising radiation' or as a very short wavelength kind of electromagnetic radiation.
Most radio telescopes look like satellite communication dishes.
The faster the object is travelling away, the greater degree of redshift. Redshift applies to radio waves, and other wavelengths, as well as visible light. The ability of a telescope to distinguish between close, but separate, objects or features. When a molecule jumps from a high energy state to a lower one, it puts out energy. This energy takes the form of a burst of light or radio waves or other kind of radiation.