Prove that the woman lost control of her mind in "The Yellow Wallpaper."
I have had to edit your question to only ask one question. Please remember that enotes does not permit you to ask multiple questions. However, thinking about the theme of insanity in this excellent short story, you will want to analyse how the woman comes to identify her own situation with the wallpaper, in the end creating an alter-ego that is trapped behind the "bars" of the wallpaper that she "releases" at the end of the tale. The woman is clearly projecting her own sense of being confined, emotionally, intellectually and otherwise, into the wallpaper, and this can be traced with the growing relationship that the narrator experiences with the wallpaper. Perhaps the most tragic moment of this short story is at the end, when this identification becomes complete, and the narrator sees herself as that woman trapped, and says to her husband:
"I've got out at last," said I, "in spite of you and Jane! And I've pulled off most of the paper, so you can't put me back!"
However, it is tragically ironic that although she declares her freedom stridently, her continued creeping round the edge of the room undercuts her protestations of freedom, making it clear that she has descended into new depths insanity. Whilst she may have "freed" the woman from the second layer of the wallpaper, this "prison" has now become real for her, as she assumes the persona of the trapped room and is left to wander around the edge of it.
One element to keep in mind about "The Yellow Wallpaper" is that it is written in the first person perspective. This entire story is told as a series of journal entries, written by the story's main character. Therefore, I'd suggest that the story's style of writing, and its method of presentation, represent a critical resource for answering the kind of question you have posed.
With this in mind, I think it's especially important to note that, as far as "The Yellow Wallpaper" is concerned, at a certain point in the story, the tone of her entries actually shifts, and her writing becomes far more erratic and manic in presentation. If you want to find evidence that the main character is losing her mind, I would suggest that one place you could look is in the story's use of language and its style of presentation, which serves to reflect its narrator's own mental state and the mental deterioration she experiences. This is one of the central conceits concerning how first person point of view functions.
"The Yellow Wall-Paper" by Charlotte Perkins Gilman is a mid-First Wave American feminist short story. The final paragraphs of the story read as the thoughts of a madwoman (and is reflective of Gilman's experience of the "rest cure" for depression, as she felt that she herself was losing control of her mind during that period). The image of the woman creeping around on the floor in a room full of torn wallpaper, not even acknowledging the state of her significant other, apart from stating that she crawls over him. The rest cure in its most extreme form involves complete bed rest with no stimulation, not even reading; the version experienced by the character in the story is less extreme but no less confining, as she is held to a single room with wallpaper that bothers her. The figures in the wallpaper are at the same time her allies and antagonists, and she in the final page comes to believe that she has become the woman that she sees in the wallpaper.