Normally waves come bundled together in overlapping groups of limited length. Overlapping transverse waves usually have their particles vibrating with random orientations so that the resulting vibration direction of the group is continually changing. Longitudinal waves can't be polarised because their particles vibrate in the same direction that the wave travels. A second polariser can be rotated in the emergent waves to check on the polarisation. When two polarisers have their polarising directions at right angles, no waves emerge from the second polariser.
Waves move energy through a medium without moving the whole medium.
Longitudinal waves transfer energy by pushing neighbours in the same direction that the energy moves. Transverse waves transfer energy by pulling neighbours sideways to the direction that the energy moves. The amplitude is half the measurement between a minimum to a maximum. The wavelength is the distance between successive maxima. The period is the time between successive maxima.