Question about Nominative/Accusative Case
So, I noticed the note in the Accusative case, pertaining to German sentence structure:
"The fact that most words in German are affected by the case explains why the sentence order is more flexible than in English. For example, you can say "Das Mädchen hat den Apfel" (the girl has the apple) or "Den Apfel hat das Mädchen." In both cases, "den Apfel" (the apple) is the accusative object, and "das Mädchen" is the nominative subject."
What happens in the event of two feminine nouns? If it were die Zeitung, for example, how do you determine which is performing the action?
"die Zeitung liest die Frauen", for example?
The cases don't avoid ambiguities all the time. There are sentences that remain ambiguous.
Your sentence, however, is not ambiguous: It can only be the Zeitung that reads the Frauen (because the verb is singular).
The ambiguous version of that sentence would require a plural verb with only plural nouns:
Die Zeitungen lesen die Frauen.
Or a singular verb with only singular nouns:
Die Zeitung liest die Frau.
(However, the "ambiguity" of these sentences does not make sense in the real world as we know it -- newspapers don't read women ;-)).
This reminds me of a nice discussion: https://forum.wordreference.com/threads/die-hat-die-forelle-gefressen.1969509/
The demonstrative article "diese" is not needed. The sentence is not very usual, though. It requires a certain context, for example:
Anna: Du sagst also, die Frau liest kein Buch? Aber sie liest doch! Was liest sie denn? Lisa: Die Zeitung liest die Frau!
Without such a specific context, the natural word order is:
Die Frau liest die Zeitung.