For the first question, think about what happens if you stretch out a slinky on the floor with a friend holding on to the other end. Stand a pen or a new piece of chalk next to the slinky somewhere toward the middle. How does the pen move when you generate a sideways (transverse) pulse? What does this tell you about the motion of particles relative to the direction of wave propagation? Do particles move parallel to or perpendicular to the direction of wave propagation?
Now put the pen INSIDE the coils somewhere in the slinky middle and grab a few coils at your end, bunching them up. Release them quickly and watch the pen. How does it move now as a result of the longitudinal wave pulse?
Do electromagnetic waves like light require a medium to carry them? How about sound? Is there an experiment that you could do to determine if a wave is a sound wave?
1. Longitudinal Waves are distinguished by virtue of the collinearity of the E / H Fields. In fact the electrostatic & electromagnetic waves travel at the same speed in one of the modes. Rather not get into a discussion of the modes as their is no relative or testable way to demonstrate some of the modes.
2. Sound waves are longitudinal. The over pressures yield a push directly from the source.