Periodic and Oscillatory Motion

No, only oscillations with a linear restoring force and sinusoidal motion are SHM. Non-linear oscillations, such as large pendulum swings, deviate from SHM.

Oscillations are larger, slower to-and-fro motions. Vibrations, on the other hand, are smaller, faster oscillations. Vibrations often occur in machines, strings, and structural components.

No, periodic motion isn't always oscillatory. It may not involve back-and-forth movement about an equilibrium point. Some known examples include circular motion in satellites or planets.