What if I like magenta? Or brown?
A rainbow gives you both red and blue; mute everything else, and you'll get magenta. That's what magenta pigments do when illuminated by white light (which is a rainbow scrambled).
No, any wave has a wavelength. You can add sin(3x) to sin(2x) and the resulting wave is a perfect fifth. Its wavelength is determined by its components; since sin(2x) has a wavelength of π and sin(3x) has one of 2π/3, the combined wave will have one of 2π.
The difference is that sin(2x) and sin(3x) are both sine waves, while their sum is not. There is no such thing as a pure tone of two merged frequencies, but there are many possible waves at any given frequency that aren't pure tones.
Here's a nice visualization of color perception (there are more modern ones, but we used the 1931 color space when I was working in the field). The horseshoe shape on the outside is the single wavelength colors.