Do all frequencies of light have the same speed?

The speed of light in vacuum is constant and does not depend on characteristics of the wave (e.g. its frequency, polarization, etc). In other words, in vacuum blue and red colored light travel at the same speed c.

The propagation of light in a medium involves complex interactions between the wave and the material through which it travels. This makes the speed of light through the medium dependent on multiple factors which include the frequency (other example factors being refraction index of the material, polarization of the wave, its intensity and direction).

The phenomenon due to which the speed of a wave depends on its frequency is known as dispersion and is the reason why prism and water droplets separate white light into a rainbow.

Since no one else has mentioned it ...

If you want to have a better conceptual understanding of the apparent slowing of light (and other electromagnetic waves) in materials, I strongly suggest reading Richard Feynman's lectures, especially Chapter 31 of volume I. That will give you much more explanation than is possible in this forum.

All the Feynman lectures are here.

And Chapter 31 is here.

Enjoy!

Recall that light can travel through a medium, like air or water or glass. You can measure the speed of light in any of these media. You can also pass light through a vacuum where there is just empty space. Think of the light coming from the sun. In empty space, all colors travel at the same speed called c. Light of different wavelengths, or colours, travels at different speeds when they travel through any medium other than vacuum. That last statement is not exactly true but the reasons are complicated and you can just look up solitons. Red light travels faster than blue in glass.