How can we read Enid Blyton books using psychological approach (Freud, Jung, or Michal Woods, for instance), and how can we relate her works to her life? Also, how are racial and gender stereotypes are clear in her works?

The psychoanalytical critical approach, particularly the Freudian approach, views the output of an author as something that can be turned back on the author herself: it is considered a reflection of the author's own deeply held traumas, fears, beliefs, repressed sexuality, childhood experiences, and so on. In this kind of interpretation, while the author's intent is not really considered, the biography of the author is very important. Freudian criticism may apply the term displacement onto figures or symbols in a text, reading the author's output as if analyzing a dream. Displacement is the shift of the author's anxieties or desires onto another (fictional) person, such that this person represents the author's avatar within the texts.

You bring up the issue of gender stereotypes, and this does indeed make an excellent starting point for a Freudian critical analysis of Blyton. In Five on a Treasure Island, we meet Blyton's most famous creations: the siblings Julian, Dick and Anne, their cousin George, and Timmy, George's dog. The main character in the novel, and the most fully developed, is certainly George, who might be considered the author's avatar. George cuts her hair short and enjoys being perceived as a boy. Meanwhile, she seems to exhibit a certain amount of disdain toward her cousin Anne, who is a traditionally feminine girl who likes to wear dresses and believes she is expected to perform household duties, such as cleaning up after her brothers.
Freudian analysis would interrogate what George and her attitudes may betray about Blyton. George has been read as a queer-coded character, and it is known that Blyton had at least one lesbian affair in her lifetime. We could, then, query whether George's rejection of traditional femininity and her refusal to abide by gender stereotypes represents a repressed sexual desire on the part of the author, or at least a desire to push against and reject the confining gender stereotypes which she could not, in real life, reject.

We can advance this idea further by considering the character of Jo, who first appears in Five Fall into Adventure. Jo is presented almost as a rival for George, and at first George resents her intensely. Jo represents a stereotypical presentation of a traveler (called "gypsy" in the text, although British travelers now consider this word offensive). She is dirty, has no parental supervision to speak of, and is perceived as a boy everywhere she goes without anyone attempting to force her to be more feminine. It is evident that George is envious of Jo. Freudian criticism would here infer, then, that if George represents Blyton's displacement—the extent of what she can dream about her own wishes—Jo is a step beyond this. Jo has a certain freedom which is connected to her "otherness." Because she is a traveler, she is already outside of the bounds of society, and is completely free. She does not have to try to be seen as she wishes to be—indeed, as she truly is. Ultimately, George and Jo do become friends, but the tension between them may be seen to represent the tension between how free Blyton can imagine her gender and personal presentation being, within white middle-class society, and how free she dreams it could be without that social constraint.

Another Freudian element we could read into Blyton's novels could be applied both to the Famous Five series and to her later series, the Secret Seven, albeit to a lesser extent. The Five series has what is known as a "floating timeline." The children, we are told, are only able to meet up to go adventuring during school holidays, which are finite, and yet they never seem to get any older. Their parents are also generally absent. A Freudian reading would question whether this represents a desire in Blyton for an endless childhood, as her own was rather difficult and marked by the separation of her parents and continuous moving from house to house. As an adult, she was also married twice; in her first marriage, both she and her husband had numerous affairs. By contrast, in the world of the Five, they are perpetually children, sexless and without even the specter of parents to mar their endless summer. A Freudian interpretation might be that, because Blyton felt unable to function as an adult, she banned adults from this dreamed universe and prevented the children from ever having to become adults.

Finally, Blyton's Malory Towers series is another excellent point of reference for a Freudian criticism of her works. Various scholars have written about the presentation of Malory Towers as a dream universe in which the schoolgirls do not seem to age, and in which the girls "pair off" into couples. "Bill" Robinson is another avatar character who is a tomboy and who behaves in a gentlemanly way toward her special friend, Clarissa. A Freudian interpretation of Malory Towers might once again question whether Blyton's own unhappy married life and lesbian tendencies led her to displace her wishes into the creation of this dream universe in which there are no men and where gender can be presented in differing ways. The girls are protected by the adults who are on the distant fringes of their universe, but they are also able to perform an innocent sort of faux-lesbianism which is, within their world, "safe."
There are many other Blyton novels to discuss, given her enormous output, but I hope this serves to answer your question.