While it is certainly technically possible to light a sphere like that it's not a good artistic choice in this instance. It doesn't read like a 3d shape, when creating sprites the number one priority is readability and number two is appeal. This light source doesn't really provide either, I highly suggest moving the light source as in yaomon's edit, obviously it's your choice if you're doing it for artistic reasons but I wouldn't do it just because it's less complicated.
The answer to your colour questions is: what looks best? Remember this is art not science.
As far as real world physics are concerned light can get hue's from many different sources, consider if you have a light source that is pure white (like the sun) then the light hitting directly on the object (the highlight) will be whatever colour the material reflects. If the light source is bright enough or the material is reflective enough this could be pure white, if the material absorbs a lot of the light it will reflect whatever colour that material is at a certain brightness based on the type of light and the materials properties, so a red object will likely have a light red highlight. But all you have to do is look around the room to see materials that change hue and brightness substantially from their darkest to lightest shade. Materials can reflect light in an infinite number of ways.
The question of why a shadow might be blue is pretty simple, if there is no light hitting a surface then it will be pure black. Obviously shadows are rarely pure black and this is because light is bouncing off every object around us, and those objects are absorbing and diffusing light, this creates ambient light which can be thought of as a base colour and brightness that all objects in a space take on. So shadows take on the colour properties of their surroundings to some degree, and based on the time of day and your environment that colour could be almost anything.
Because we can't account for all of these variables without a degree in physics most artists just go with their gut, if a white highlight looks right then white it is. And being accurate to the real world doesn't necessarily produce the best looking art, all choices are based on the real world but the artist decides whether to obey those rules or not for the sake of more aesthetically pleasing results.
I suggest you take another look at yaomon's edit and consider what you like about it, rather than what you don't. Everyone here is trying to help and their advice is certainly taking into consideration that you've made your choices, but that doesn't necessarily make them the best ones.
