Skin is a good thermometer. The period of oscillation depends on the amplitude. The restoring force is constant at all points in the oscillation. The heavier a pendulum bob, the shorter its period. All pendulum motion is perfect simple harmonic motion, for any initial angle.
Harmonic oscillators go forever.
A pendulum accelerates through lowest point of its swing. The acceleration is zero at the end points of the motion of a pendulum. Waves transport matter. There must be a medium for a wave to travel through. Waves do not have energy.