Is Vanka's perspective on the people around him mostly reliable, or mostly guided by exaggeration?
As a child who has been sent away from a comforting home, the emotional Vanka may be guided by an extreme, even distorted view of the world. He may, in his disorientation and loneliness, be overplaying the positive qualities of his village and his grandfather, and may conversely be exaggerating some of the harsh treatment he receives as an apprentice. After all, Vanka takes offense at minor chores (like cleaning a fish) and does find exhilaration in his Moscow settings.
But an equally strong argument can be made in favor of Vanka's veracity. His memories are extremely lucid and he has apparently reached a breaking point despite enduring tough treatment previously. Indeed, "Vanka" can be read a faithful record of abuses, delivered by a boy who has endured too much—not by a boy distorting everyday troubles into abuses.
How does Chekhov prevent "Vanka," which after all focuses on a lonely orphan, from becoming simplistic or sentimental?
Chekhov's short narrative could have been rife with melodrama, in light of both its subject matter and its dramatic movement from sorrow to hope. However, Chekhov tempers such obvious emotions in a few different ways. "Vanka" can be treated as a clever study of voice, perspective, and memory: the real interest of the story is not what Vanka feels (which is fairly obvious throughout) but how Chekhov captures Vanka's psychology and viewpoint, moving deftly from present to past and back again. Moreover, Chekhov complicates the more blatant emotions in Vanka with hints of comedy, complexity, and ambiguity. He dedicates significant portions of the story to earthy and amusing characters, such as Eel and Vanka's grandfather, and even suggests that Vanka himself (who is intrigued by certain aspects of Moscow) is more ambivalent than he at first appears.
Should Chekov have expanded "Vanka," or does the story work best at its current length?
One of the remarkable features of "Vanka" is the relatively large, relatively diverse, and consistently well-orchestrated cast of characters: Vanka, Alyakhin, Eel, Konstantin Makarich, and Olga Ignatyevna all make quick yet lasting impressions. In light of such efficiency of presentation, "Vanka" can be considered a success at its current length, a length that also allows Vanka's emotions to register with exceptional lucidity and directness. Expanding the story might have undermined these virtues.
However, a longer narrative might have allowed Chekhov to trace Vanka's development in more detail, perhaps yielding a story closer to Chekhov's own short novel "The Steppe" but with the added virtue of a dynamic urban setting. Indeed, expansion could also have been a means of fully analyzing of the social and cultural issues (such as the role of religion in everyday life) that are mentioned in passing in "Vanka."
Is the relationship between Vanka and his grandfather mostly distant or mostly close?
It is possible to see Vanka and his grandfather as two characters who share an important bond: Vanka remembers his grandfather vividly, recalls helping his grandfather with the Christmas tree, and reaches out to the old man in an earnest, emotional manner.
Yet there are solid arguments for the opposite positions. Vanka, after all, only has one memory (the Christmas tree) that shows anything like a close interaction with his grandfather. His and his grandfather's real affections may lie elsewhere—with Olga Ignatyevna or with the cooks, for instance—and the letter may best be understood as a plea to the only well-inclined figure Vanka has in his life, not to a man with whom Vanka shares any exceptional relationship.
Does "Vanka" have any important sociological or ideological messages, or is it best understood as an intensely specific portrait of one character?
Because it focuses so much on the feelings and perspective of its protagonist, "Vanka" can certainly be read as a non-political story.
Nonetheless, Chekhov does gesture towards a variety of social themes—class differences, religion, the movement from country to city—that demand analysis. It is possible to take such issues mostly as background, as inevitable in a realistic character sketch such as "Vanka" but as secondary to Vanka's inner life. Yet a more sociologically or ideologically analysis can take the cruelty of Alyakhin as a statement on religious hypocrisy, or Vanka's movement from country to city as a statement on the shifting nature of 19th-century Russian society.