Hello Tom, it's good to see you. I would omit "as" in nos 1 and 5; but I can imagine that some speakers would use it. In 2 and 3, on the other hand, I would expect most users to include "as"; while all would omit "as" in the 4th.
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Mr. Tom The Sunday Times has judged her as one of five most beautiful women in India. This doesn't work for me. I take it that she is accepted as one the etc., and they then proceed to judge her on some other basis.
I would say,
AvangiMirror mirror on the wall, who is [the] fairest fair of all?And that's why it is optional here
(At least it scans better without it!)