Your question includes a number of elements that cannot be answered by reference to the story, but I will try to answer those elements that Faulkner discusses.
Miss Emily is identified in the story only as Emily Grierson, and although it would have been common in the south at the time for a man or woman to have a first, middle and last name, Faulkner uses only her first and last names. Her age is not discussed, but there is some evidence, based on a computer analysis of the chronology in the story and Faulkner's own drafts of the story, as well as his notes about its composition, to believe that she was born around 1850 and died in about 1924, making her 74 years old at her death. Where she is buried, or when her viewing was, is not possible to determine based on the story.
Emily, based on evidence in the story, was born and raised in the town of Jefferson, but no state is mentioned. Based on Faulkner's other stories and novels, we can assume that the state is Mississippi, the state in which most, if not all, of his stories take place. As to her parents, the only parent mentioned in the story is her father, and he is never named. Because Miss Emily is a Grierson and never married, we can safely assume her father was a Grierson, but that is all we can deduce about her parents' names.
Because Miss Emily was part of the southern upper-class around the time of the Civil War, her schooling would most likely have been in the home with tutors rather than in a formal educational setting. In any case, Faulkner is silent on Emily's education, but a woman of her class would have been educated in music, the arts, some literature, and management of a household. We know that, later in life, Emily taught China painting, so it is reasonable to say that she had some art training when she was young. As a woman of the upper-class, Emily would not have worked outside the home, so the concept of employment is not relevant to Emily's life.
Her "significant other," which is not a term that applies to Miss Emily's and Homer Barron's relationship, could refer to the northerner who came to Jefferson and began a relationship with Emily, Homer Barron, but the relationship is impossible to characterize accurately because Faulkner never actually discusses the relationship. We can infer, though, that they had some sort of "courtship," which, because of Barron's nature and Miss Emily's obsession, resulted in disaster.
Emily's personal traits are difficult to discuss with any certainty, but, based on the episodes Faulkner gives us, we can reasonably argue that Emily is shy, reclusive, obsessive, repressed, intelligent, and, to put it bluntly, a bit crazy.