longitudinal an example of light- wave, particles move back&forth perpendicular to the direction of the wave?

Answer 1

Yes light (and other electromagnetic waves) is an example of a longitudinal wave. Although be careful talking about the particles as light can travel through a vacuum therefore no particles!
(wave-particle duality is a minefield!!)

Answer 2

The question of longitudinal or transverse waves comes only in case of mechanical waves in elastic media. Light is not a mechanical wave. It is an electromagnetic wave. Since it can move without a medium, the movement of particles back and forth also does not arise.