1. Both
Assuming we are talking about a longitudinal wave (where particles oscillate in a direction parallel to the direction of motion of the wave), the answer is 'both'. In fact, waves consist of oscillations of the particles of a medium: in the case of the longitudinal waves, the particles oscillate back and forth, back and forth, continuosuly. This means that at some time they are moving forward, while at some time they are moving backward, with respect to the direction of the wave.
2. The amplitude
The energy of a wave is related to its amplitude. More specifically, the energy of a wave is proportional to the square of its amplitude:
therefore, if the spring has a larger amplitude of oscillation, it also has more energy.
3. Yes
Forces of friction act while a mechanical wave passes through a medium. As a result, particles during the oscillations lose part of their energy: this means that the amplitude of the oscillations of the wave decrease over time, because the wave loses some energy. Eventually, if the friction lasts enough, the wave can lose all its energy.