A mechanical wave generally does NOT require a medium to propagate.
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Sound propagates through a longitudinal wave, a type of mechanical wave.
Yes, a sound wave is a mechanical wave. Sound waves need a medium (like air) to travel through. The energy of the wave, the mechanical energy, is transferred into the medium through which it is propagated.
Sound travels in longitudinal waves, which means that the particles of the medium move in the same direction as the wave is propagating. This is in contrast to transverse waves where the particles move perpendicular to the wave's direction.
Radio waves are electromagnetic. That's how they can get down here from satellites.
Light is an electromagnetic wave. It consists of electric and magnetic fields that oscillate perpendicular to each other and to the direction of the wave's propagation. This is in contrast to mechanical waves, like sound waves, which require a medium to travel through.