Conception behind sharingan is simple, If you consider Indra succeeded Hagoromo's yin, and Asura, yang. You can rephrase it as saying, Indra inherited the mind, and Asura the body. As such sharingan is deeply rooted in the Yin side, awakening sharingan and progressing through it stages all require emotional development.
Awakening and progression up until 3T require some emotional trauma. I include progression because even that is accelerated over emotional development noting Sasuke's progression to 3T during battle with Naruto.
Mangekyou Sharingan requires another trauma, death of a close relative.
Tobirama explains the changes in mental chakra created through trauma awakens sharingan.
As i explained before, Sharingan evolves to Rinnegan upon eliminating genetic deficiencies. I.e. Senju genes. Then there is EMS to consider in between but that's not necessarily a stage of progression as much as a perfected MS.
So in conclusion
Rinne Sharingan >Rinnegan > Asura's Dojutsu (represented as a Mangekyou in the anime) > Mangekyou(+EMS) > 3 Stages of sharingan.
Sharingan can see chakra. It's effectiveness depends on the skill of user, if the user understands how chakra natures work. They can take it as far as to predict the incoming chakra nature (element). i.e. You can predict determine a technique is lightning release by looking at whether or not the chakra particles are vibrating intensely. Friction between particles on the other hand would mean Fire release. So the answer is no, it cannot directly predict the nature and type of attacks. It lends the tool that allow the user to predict.
Visual prowess of Sharingan when compared to Byakugan is tricky question. You have to look at each case separately. For instance Byakugan dominates when it comes to range, it doesn't have a cone of vision like sharingan does. It has 360 degrees of vision with one blind spot.
Sharingan on the other hand provides a stronger reaction time and affinity towards genjutsu as well as hypnosis.
Both Dojutsu can see chakra and through objects but Sharingans ability to see through objects is more limited than byakugans. Some idiots will tell you that you can see the color of chakra and tell which elemental nature opponent is using. But thats false, elemental nature can be predicted like i previously explained and colour has more to do with the type of chakra (a third component like NE?, Bijuu's chakra, changes in ratios like Sasuke 's Yin heavy chakra being colder and darker in colour.