Asking for a discussion of a book's "qualities and problems" is a somewhat vague request, but I will do my best to address it. Three qualities of the book stand out for me, and certainly, the characters have many problems that can be discussed.
One quality of The Secret Life of Bees is that it is what we call a coming of age story, meaning we follow a character who gains maturity over the course of the book. Lily is such a character, setting out on a voyage that results in her learning about the world and about herself, beginning as a child in many ways, and growing in her understanding of herself and others by the end of the book. At the beginning, she is a rebellious teenager, but she learns to have empathy for others and to assume responsibility for herself.
Another quality of the book is that it shows that we all need mothers, or, at least, someone to mother us. Lily sets forth to search for her mother, and really, Rosaleen is lacking a mother figure in her life, too. By the end of the book, both characters have found a mother in August Boatwright.
Yet another quality of the book is a spiritual one, with Lily and Rosaleen being introduced to the Daughters of Mary, Black Mary being a symbol of a higher being, and a more meaningful symbol, because she is a female representation.
Lily's problems in the book are many. She is motherless. She carries the guilt for being motherless. There is a mystery surrounding her mother's leaving that she must solve. And her father is abusive. These are a great many problems for a teenage girl to grapple with, yet by the end of the book, she has done so quite well.
Rosaleen's problems are largely the result of the time and place in which the story takes place. She wants to exercise her right to vote, but as an African-American woman in the sixties, in the rural south, this is not so easily done. And once she and Lily are "on the run," she is in further jeopardy because of her having stood up to white men and because she has the burden of being responsible for a white, teenage runaway. Yet she, too, finds a safe harbor with the Boatwrights and a life for herself by the book's end.
There are certainly other characters with problems in the story, for example, May, who was irrevocably damaged by racism and the loss of her twin, and June, who carries great bitterness in her heart. T.Ray, too, has many problems, which manifest themselves in abusiveness towards Lily.
A one-page paper on the qualities and problems in this book could use some of these ideas or others that you might think of yourself. The book has many themes, and the biggest challenge will be to keep an essay to just one page!