This is a good question, and I think you may benefit from an answer without a lot of technical or mathematical detail. At a basic level, the mess of color spread all over that you describe is exactly what a near sighted person sees without their glasses, or what a camera sees without its aperture and lens.
The reason your eye can resolve images is that your pupil is very small and blocks the vast majority of the light coming from any object except a narrow slice. Then, the little bit of light that makes it through is further focused to an even smaller point on the retina.
Your point about light rays crossing is not a problem, because the light passes right through other light without interacting.
Here is a video that may help you https://youtu.be/OydqR_7_DjI
EDIT: I think after reading thru all this, I may finally understand better what you are asking: Given, say, your 2nd diagram, how does your brain "know" where the ray of light is coming from, when it could have originated from any point along the ray? The answer lies in neuroprocessing rather than physics. From a purely physics standpoint, it is true there is no way to "know" simply from the incoming light where the object is located. The mind relies heavily on context (comparisons with other objects in the visual field, perspective) and memory to make organize objects in space into a meaningful image. If you stood in a black room or space devoid of anything but one or two generic points of light, it would be impossible to determine how far away from you or from each other they are. You coldcould only tell the angular separation, but it could be two distant stars, or one star and one Christmas light 20 feet away, or two Christmas lights. That is why if you look up at the stars on a very dark night in a remote area, they seem to be at ceiling height, just above our heads (I've found) even though they are light years away. But if you take that second ray image and add a lens, so the refraction is correctly drawn geometrically, instead of your hand drawn sketch, orit will help you see how point sources of light can both converge without being conflated. Viz.