1) A wave travels from one point to another and transport energy.
2) Depending on the type of wave, some waves called mechanical waves travel through a material medium. Electromagnetic waves travel through vacuum.
3) The difference between Transverse and Longitudinal waves is that a Transverse wave travels in such a way that the disturbance causing the wave is perpendicular to the direction at which it is travelling. For a Longitudinal wave, the disturbance causing the wave is paralle to the direction at which it is travelling.