Amplitude is the height of the wave from 0 displacement (normal) to the peak, where the peak is the highest point. The Wavelength is the distance from the start to the second point the wave passes 0. i.e. a complete wave.
Period: if it was a displacement/time graph, the period would be equivalent to wavelength, so period is the time for the wavelength. The frequency is 1 / period and measured in Hz (1Hz = 1wave per second)
The Wave Equation
The oscillation/vibration is at right angles to the direction of travel. An example of transverse waves are electromagnetic waves
The oscillations/vibrations are along the line of travel.
Are mechanical waves because it actually moves particles. E.g. sound waves.