Anna, I have made some more changes to your submission below. Words that I changed are in UPPER CASE, words that I removed are replaced by "___". Most of the changes are corrections to your use of definite and indefinite articles:

“Heart of a Dog” is A [1] novel by THE famous Russian author Mikhail Bulgakov written in 1925.
Moscow, 1924. The successful surgeon professor Philipp Preobrazhensky conceived an unprecedented experiment. He PERFORMED [2] the transplant surgery of a human pituitary gland and human testicles to a dog.
THE experimental animal was a homeless dog named Sharik. THE organ donor became a thief, THE rowdy and ___ alcoholic Klim, who was killed in a brawl.
The results of this experiment exceeded ___ all expectations. The dog took a human form. THE new creation called itself Sharikov. Unfortunately, Sharikov inherited ___ all Klim’s addictions.
Eventually he became so dangerous to others that the professor PERFORMED [2] a new transplant surgery and turned Sharikov into the dog again.
The director Vladimir Bortko made a great movie on this story, which perfectly conveys THE flavor of the time.
Here is a frame of the film. It’s the former dog Sharikov.

1. If you say "the novel" it implies that Mikhail Bulgakov only wrote one novel. It is better to say "a novel", since I'm guessing it is only one of several novels that he wrote.

2. A surgery is a procedure, so you don't make or produce it. It sounds better to perform or maybe carry out a surgery.

Great job! Articles require a lot of practice to be used correctly )))

Heart of a Dog

“Heart of a Dog” is the/a (the is ok if it is specifically the singular novel written in 1925) novel by famous Russian author Mikhail Bulgakov, (put a comma here for 'a' and no comma for 'the' hahaha) written in 1925.
Moscow, 1924: the successful surgeon professor Philip Preobrazhensky conceived an unprecedented experiment. He produced experimented with the transplant surgery of a human pituitary gland and human testicles to a dog.
An The experiment's animal subject was a homeless dog named Sharik, and a dead thief name Klim  became a thief, (a rowdy and an alcoholic Klim, who was had been killed in a brawl) became the organ donor. 
The results of this experiment exceeded the all expectations. The dog took a human form - a new creation calling itself Sharikov. Unfortunately, Sharikov inherited the all Klim’s addictions.
Eventually he became so dangerous to others that the professor made invented a new transplant surgery and turned Sharikov into the a dog again.
The director Vladimir Bortko made a great movie on this story, which perfectly conveys a flavor the atmosphere of the time.
Here is a frame of the film. It’s the former dog Sharikov.

Anna, you did a great job with your post.  The only thing that I would correct would be the use of the word 'the'. "The results of this experiment exceeded the all expectations." and "Unfortunately, Sharikov inherited the all Klim’s addictions."  The proper English would be "The results of this experiment exceeded all expectations."  The article the is not needed.  The next sentence reflects the same principle.  "Unfortunately, Sharikov inherited all Klim's addictions."  I hope this helps.