Pertaining to "The Lady with the Little Dog", I don't think it could be called exactly an autobiographical story, but it has obvious parallels to Chekhov's life. I don't know if they were worked into the story consciously or unconsciously, but I think they are definitely there. For example, at the end of the story he writes:
"And only now when his head was grey he had fallen properly, really in love -- for the first time in his life."
Gurov's path to "love" -a series of mostly physical relationships with a variety of different women before finding a marriageable mate- shadow's Chekhov's life. Chekhov had numerous liaisons, some sexual others not, with a really wide range of women, including even a pair of bi-sexual actresses, and two or three sets of "three sisters".
That being said, I don't think that Gurov is really at all Chekhov embodied in fiction. This is evident in Gurov's attitude toward love. It is more optimistic, hopeful, or, better, anticipative than Chekhov's. Even when Chekhov married Olga Knipper, I feel, that he wasn't enamored with her the way Gurov is with Anna. Chekhov definitely had a very fond affection for her, otherwise he wouldn't have married her (a step he was very cautious of taking); but, in his letters to and about Knipper, he never uses the rapturous language that Gurov sometimes does.