"Wave speed is determined by the frequency of the wave." - Incorrect. Wave speed is determined by the medium through which the wave is traveling, not the frequency.
"The amplitude of a wave affects its speed." - Incorrect. The amplitude of a wave does not affect its speed, but rather it affects the intensity or energy of the wave.
"All waves travel at the same speed in a vacuum." - Incorrect. The speed of light waves in a vacuum is constant, but other types of waves (like sound waves) can have different speeds depending on the medium.