What is the difference between "is speaking" and "is talking"?
No difference. In some contexts, one word may be preferred over another.
Why isn't it 'La femme est parle?' Why is 'is' omitted?
You don't need verb "être" with the French simple present. For details, please refer to what I explained above.
which french word has a meaning of "say"?
'The women speaks' is also correct right?
"The woman speaks" is a correct answer.
Why not the woman is talking?
That is also an accepted answer.
No surprises then!