Does circular polarized light with same screw like that of the chiral material always reflected or only under specific condition? What is the Jones matrix describing propagation through chiral material?
My best guess: you haven't yet gotten what the meaning of 'chirality' is. And - unfortunately - there are several types of chirality - even when concentrating on 'optical acitivity'. But none of these has a significant impact on 'reflection'.
'chirality' in terms of 'light' could be:
Circular dichroism: in short a difference in light absorption depending on the orientation of circular polarized light. See https://en.wikipedia.org/wiki/Circular_dichroism
'optical activity': this is the property that's normally thought of when talking about 'chirality': basically, chiral materials showing this property exhibit different propagation speeds (resulting in different refractive indexes) for left- resp. right-hand circular polarized light. See https://en.wikipedia.org/wiki/Optical_rotation
And the very basic page about chirality:
https://en.wikipedia.org/wiki/Chirality
Regarding your questions:
Aside from an eventual difference in reflection due to the difference of the refractive indexes, there is NO reflective property inherent to chiral materials.