OK so, the keys on a piano are black or white, right? The white ones are A B C D E F G. The black ones are either sharp or flat, let's not worry about why for a second and just say the black keys are Ab Bb Db Eb and Gb.

If a song is in the key of C, then, very simplistically, almost all the notes and chord are *only* comprised of the white keys. That is, a "key" is 7 out of the available 11 notes. Those notes sort of "sound good" together and most western music is oriented around a key.

Different keys are different note, but the 7 notes in that key have the same relationship as in the key of C, just shifted up or down.

Yes, the order is always the same. The refraction that happens in a rainbow isn't actually "splitting the light into colors," it's actually just taking white light (which is a combination of all the visible wavelengths of light) and spreading them out like an accordian. So, the colors you see will be ordered by the wavelengths of light.

Low frequency light wavelengths that we can see start at red and as the frequency increases you get up into orange, yellow, green, blue, etc.