To be short I have not been able to progress far on my own. How do I go from this Chao model to that Chao model? How does one get the same textures and coloring?

How do I get the eyes to sit on the face? Right now when I pull them close they merge into the model.

Getting the colour right is a matter of skill, and it has nothing to do with the modelling, but rather the lighting. dont expect to get the right colour in the viewport.

when it comes to the model, well its hard to tell how to make it look natural. the easiest way i think would be to use a texture, but it can also be modelled, in which case the eyes should be a separate mesh, but still follow the curvature of the skull, i think shrinkwrap followed by a Solidify modifier would be a decent solution.