I added bones started from a single bone (first “pic”) to a very simple character instead of using the add-on rigify (second “pic”). The third “pic” is generated from second “pic”.
My problem is how to generate rig like the third “pic” from the bones I made?
If you want to generate your rig with rigify, in my opinion, the easiest way is to use the human metarig.
If you absolutely don’t want to use the human metarig, another solution could be to add each body part to your base skeleton with the rigify buttons (eg : biped arm, biped leg …) and then you will be able to generate you rig with rigify.
No, rigify does not create any eye tracking bone.
Anyway, you can easily add some extra bones in a rigify generated rig and an eye tracking rig is not that complicated to create, in my opinion.