Why does Freida survive her abuse and Pecola goes insane?
This is truly a hard question to give the one "right" answer to your questions because it is so interpretive. "Why did Tony Morrison create one character to react in one way in contrast to another?" is basically the question you ask, and truly, in my opinion, the only "right" answer could come from the author herself. You have more than one true question, and I'll tackle one of them for you: Pecola's insanity. After much thought, I came up with my humble opinion and possibility.
It is clear, through the themes explored in the Bluest Eye (those concerning race, equality, loss of innocence, and acceptance), that one character stands out above the rest: Pecola. She is undoubtedly the main character, the protagonist, the character that speaks loudly to the reader and one whose internal and external conflict are most revealed.
Smiling white face. Blond hair in gentle disarray, blue eyes looking at her out of a world of clean comfort. The eyes are petulant, mischievous. To Pecola they are simply pretty. She eats the candy, and its sweetness is good. To eat the candy is somehow to eat the eyes, eat Mary Jane. Love Mary Jane. Be Mary Jane (Morrison 50).
Pecola is convinced of her "ugliness" and her community condemns her without hesitation. Her instability, her anguish and pain shared through her struggles, make those around her, the other main characters, feel better about their own situations. This story is all about "perception" and how people see themselves and view others. Pecola was the most vulnerable and the most susceptible to the desire of "whiteness" represented through having the "bluest eyes" ultimately changing her life. And, when this did not happen, and after surviving the violation of her father, the bearing of his child, and the ostracizing of others, she had nothing except herself. In other words, she turned inwards away from the others to the only place where should could no longer feel pain and disappointment: a world of her own, otherwise known as insanity.