A mechanical wave is an oscillation $($periodic motion$)$ that travels $($propagates$)$ through a medium and:

The wave motion transports $($carries$)$ the energy without carrying any mass;

The wave moves with the same speed $($when it propagates$)$ in the same medium;

The wave changes its speed when entering and then moving through $($propagates in$)$ a different medium;

All these above answers are correct.