One noteworthy thing about all of Katherine Mansfield's writings is that she is generally less concerned about plot than she is about her characters and the themes she wants to convey. The themes she most explores are isolation, loneliness, love, and gender roles, and these themes are universal. She often blames society for many of her character's problems, especially in its rigid adherence to the role of women in her society.
Mansfield's characters in each of the works you mention are trapped in some way by the constrictions placed on them by Victorian society. In "The Doll's House," those restrictions are based on class (money), as the Burnell children discount the Kelvey children in all sorts of horrid ways, and their isolation is not only social but physical. (You didn't mention this text, but this theme of the isolation caused by class distinctions is also explored in "The Garden-Party.") Miss Brill is dismissed and isolated not primarily because of class but because of her age. Leila is isolated in part because because of her youth, and Miss Meadows is, at least temporarily, isolated by her grief.
Most of these female characters are also rather trapped in the role society has structured for women. Miss Brill is an unmarried woman, so of course she has to be a teacher. Leila is at the mercy of the men at the ball who have to "claim" her in order for her to dance. Miss Meadows is at the mercy of a man who boldly proclaims that he is disgusted at the thought of marriage, and she is desperate enough to say:
"But, my darling, if you love me," thought Miss Meadows, "I don't mind how much it is. Love me as little as you like." But she knew he didn't love her. Not to have cared enough to scratch out that word "disgust," so that she couldn't read it!
Each character is, in some way, restricted by the confining role society has given women.
Mansfield also uses symbolism consistently in her work, and of course that fact alone is enough to connect them (i.e., if you find symbols in all her work, symbolism connects them).
The primary symbol in "Her First Ball" is the music. Just as the tempo and rhythms change, so do Leila's emotions. In "The Doll'd House" of course the significant symbol is the dollhouse, the representation of everything the poor Kelveys cannot have now and presumably will never have because of their social and financial position.
The unmistakable symbol in "Miss Brill" is the fur, representative of the woman herself. It is taken out of the closet and out of its box each week and put on display. It is distinctly old, shabby, and worn, yet she does not seem to notice (or care) and wears it with pride. Each week she comes back home and puts the fur back in its box where it will wait for another week before it is free again. The same is true of Miss Brill, of course; however, once she is forced to realize that she is one of the actors in the play she had been so happy to observe, her world crumbles and her joy is gone. She slowly puts the fur in the box, and
when she put the lid on she thought she could hear something crying.
One of the symbols in "The Singing Lesson" is the song Miss Meadows has the girls sing, "The Lament." It is a reflection of her emotional condition after being rejected by her fiance, though the entire tone of the song changes once she learns that he "must have been mad."
Each of these stories is recognizable as a Mansfield work, at least in part, because of her consistent characterization and use of symbols.