In vauum, all the electromagnetic waves have the same speed $c$. When the wave passes through a material, such as the glass of a prism, the speed is decreased, but only during the passage, inside the material. When the wave exits from the prism, its speed comes back to the speed $c$ (or slightly less, if the wave is propagating in air instead of vacuum).
When the wave enters into the prism, it keeps its frequency (how many periods per second). But, since it is slowed down, its wave length becomes shorter: in a period, it travels a shorter path. But, also in this case, when the wave exits, it takes back its wave length, the same it had when it entered.
Coming to the second question. It is useful to think that the color of the light is associated to the frequency, which never changes in refraction, reflection and diffraction processes. Frequency is important because the "sensors" in our eye are sensitive to the photon energy, which depends on the frequency. On the other hand, the speed of light in our eye depends on the material of the eye itself, so there is also a well defined and fixed relation between wave length and frequency!
So said, a beam with a given color, after passing through a glass prism or a lens, will still have the same color. Of course, its wave length will change along its path, but our eye will never know it.
Finally, what does it mean that a beam is the superposition of various wave lengths? This would deserve a separate question, but this can help to understand the principles:
https://demonstrations.wolfram.com/SuperpositionOfWaves/
Best Answer
When light enters glass (or another transparent material), its frequency stays the same and its wavelength changes.
In a comment, you say that you are using "color" to mean "wavelength". Well, I think you are using the word "color" incorrectly. According to a normal definition of "color", the color of light does not change when it enters glass. But the wavelength does.
ADDENDUM: Color has to do with how light appears to you when you see it. You can't see light while it's in the prism, you only see it after it exits the prism and enters your eyeball. Yes, the wavelength changes when the light enters the prism, but it changes right back when it exits.