How does the narrator's mood change as "The Yellow Wallpaper" progresses?If psychologically focused on unnamed narrator of the story how is this...

You have raised a great many interesting issues in addition to your basic inquiry. To answer the basic inquiry, the narrator becomes increasingly irrational as the story progresses, until she appears to be out of touch with reality, however, not so out of touch with reality that she does not stop to think that she would not do something desperate. She says "a step like that is improper and might be misconstrued" (255).  

Several other points you raise are important.  The story was published in 1892, when women had few rights.  They did not vote, did not generally own property unless it was held with their husbands, and even that was rare. To the degree that they were educated, it was only so that they could meet and attract husbands.  You will notice that the husband in the story treats the narrator more as a child than as a wife, and while this is exaggerated, there appears to be some validity to the idea that women were treated almost like children in this era.

I do not think, though, that the fact that the narrator does not kill herself is evidence that she is not mentally ill. There are probably millions of mentally ill people who do not commit suicide.  There is evidence that the author suffered from post-partum depression, and I believe that is what is being portrayed in the story.  This is not a condition that was recognized at the time, and it is often not recognized by friends and family today.  As to treatment for mental illness of any kind in that era, the options were limited, and probably rest and a lack of stimulation were typical prescriptions for anyone.  While I have no particular expertise in that era, I have done enough reading to be able to say that mental illness in women was taken less seriously, since most of their behaviors were attributed to their being women, who were thought of as more emotional, less stable, and less competent generally. The origin of the word "hysteria" is from the Greek word for "uterus," good evidence of the idea that females tended to the hysterical simply because they were female. Sometimes I am not so sure that much has changed since that time.