The blue color of the sky is due to Rayleigh scattering. As light moves through the atmosphere, most of the longer wavelengths pass straight through. Little of the red, orange and yellow light is affected by the air.

However, much of the shorter wavelength light is absorbed by the gas molecules. The absorbed blue light is then radiated in different directions. It gets scattered all around the sky. Whichever direction you look, some of this scattered blue light reaches you. Since you see the blue light from everywhere overhead, the sky looks blue.

Now on to your primary question. There are two types of treaties: Research and Economic. Every civ gets one of each. If you choose to gift/trade/sell a treaty to another civ, they will receive 10% of your research/economic output. This costs you nothing. It is 'found money', as it were.

These treaties do indeed strengthen relations. Only allied civs have closer ties.

Yes it does. As an added bonus, you'll get a permanent relations hit as someone who back stabs friends. I think it's with all races. So stab those whom you have treaties with...last.

I use my treaties to butter up my neighbours. The two races I feel are most likely to declare on me get the treaties, while I can then focus more on research (with a weak military), out-tech them, and by the time they've got angry enough at me to declare war, I'm able to crush them.

You can also use them to booster a weaker race to make them a bit tougher, and of course if you receive them they provide a valuable boost to your own economy/research.

Have you seriously ever negotiated for a planet? More than one? I have never successfully done this. Either I don't have enough BC or they want the world of tech just to give it too me. I usually figure that it is just as easy to take it from them.

But I also want to play a trade/manipulating game one of these times. You know, where the end result is that everyone bows down before me and gives me lots of stuff for free and without me ever firing a shot.

Actually the basis is the physiology of the eye. Our retina contains three different types of light receptors for vision at daytime (cone cells) that each have distinct sensitivity for a definite range of wavelengths. It is a distribution of probabilities if a rexceptor gets activated by a photon with a distinct wavelength, each type having its own most likely set of wavelengths to be activated from. The cone cells have 3 subtypes, with the S-type being activated in blue wavelengths, the M-type in green and the L-Type in red wavelengths. This is represented in the RGB-color scheme which you may find in context with monitors and other visual technology. The perception created by your brain is not which receptors get activated, but what the relation of the activation of the receptors to the others is. Your brain calculates the relative activation of each receptor type in relation to the others and translates it seamlessly into a perception of color. This is the physiological basis of the RGB-system, which uses red, green and blue light in different ratios to create the sensation of colors.