"This is a sad girl."
Translation:זאת ילדה עצובה.
No, there is no inconsistency there. It goes like this:
This is a sad girl - זאת ילדה עצובה.
This girl is sad - הילדה הזאת עצובה.
As for the rest of your question, it would go like this - using the adjective sad:
A sad girl - ילדה עצובה
A girl is sad - ילדה היא עצובה
The girl is sad - הילדה עצובה
The sad girl - הילדה העצובה
This pattern is for any adjective.
As for זו, it's the same as זאת, as you can see from other comments here. They are both feminine forms of "this". The difference between them is that זו is more formal, and used less commonly.