but, why does this produce something that causes us to be able to see ? And this causes me to wonder, how are light and vision related ? I think they are deeply related, actually. And, what is a true vision then ?
You're asking some of your questions from the wrong pov. The sun doesn't shine in a way such that eyes can see it, it's the reverse, something about us means we 'see' [and thus perceive] a particular part of the spectrum.
It's because we, and thus our eyes, evolved on a planet near a star that has a peak radiation in that part of the spectrum. Hence our eyes now see, and what, as a result, we call visible light [the atmosphere blocks parts of the sun's radiation as well, so that will have been significant too, no doubt]
So, it isn't the light that is special [compared with other parts of the spectrum] it's us and the circumstances in which we happened to evolve that were.
Bats see objects by bouncing sound off them and interpreting / perceiving their surroundings from what they hear. Our eyes are sensitive to the radiation [in various different ways that wikipedia / google will tell you much better than I will] which is bouncing off things all around us [and being emitted by some too] and our brains interpret that input to give us our perception that we call sight.
Aside from that, light isn't particularly special compared with other parts of the spectrum that aren't visible.
[That said, the various parts of the spectrum do differ when they interact with surfaces - which is why we can xray ourselves. This is another function of the wavelength, but it's also related to the intensity of the radiation and the composition of the surface it hits [or doesn't hit in the cases where it travels straight through

]
As for what causes the sun to shine, very basically, gravity collapses the sun's matter to the point where fusion begins [and this causes an outward pressure, the size of a star is, more or less, the balance between gravity and that outward pressure caused by the reactions inside. When a star runs out of fuel this changes, as a function of its mass] These reactions inside the star radiate energy, which eventually leaves the surface and, some of which, we see as visible light. 'Visible' is really to do with the temperature, e.g you can feel a baby radiates heat, because they are warm, yes? But you don't see them glow. If you put an iron bar in a fire eventually you see it glow.
I know that colors are within light, but they don't actually *cause* light, right ? How does it all relate ?
Colours relate to different wavelengths of the visible [i.e the bit we call light] spectrum.
It's our perception [and the fact we have cones in our eyes that are sensitive to different wavelengths] that sees colours. For objects that are reflecting light, we see their colour as the wavelength(s) they reflect when light hits them.
So it's probably better to say the light is of a particular colour, rather than colours are within light. For sunlight though, as you might have seen in a rainbow or prism, the light is made up of more than one wavelength. This spectrum of colours in the sunlight relates to the makeup of the sun, it's temperature and things like that. Scientists use the spectrum of distant stars to find out the same information.