I have cared a lot of cats, and I didnt knew about all that experiences, but I did a lot about this with my pets. I put a mirror in front of the cat, and watched the reactions. The pattern is 90% the same:
1) The cat looks surprised. Depending of the the natural character of the cat, he will watch the reflex or get "armed" to fight. Cleary he think its another stranger cat.
2) The cat then try "feel" the reflex, touching sometimes, smelling other times, and ever trying look behind the mirror
3) Finally, the cat probably detects the reflex is not a threat and lose the interest
I really dont know if has some part of "self awareness", but probably the cat lose the interest really far before any of this level of perception
Other point is, the cat trust more in the sense of smell and hearing than the sense of view. Only one image is not enough to "identify" a target.