Bavarian Fire Drill: Jolly U and Rat tell Albina they are from a psychiatric hospital for dangerous children, and Alisa, the most dangerous person, has escaped. Albina gives them the information they need.
The Bechdel Test: Passes. Alisa and Yulia, while in the hospital, start by talking about where they are from, and then talk about food. Later on, they talk about Kolya and other boys, but not in a romantic sense, as they are trying to figure out which Kolya is the one who visited the future.
Big Damn Heroes: The children come to save Kolya from the pirates, Marta Erasovna steps in to defend the children against the pirates, and then Polina appears from the future to arrest the pirates.
Chekhov's Gun: The Mielofon. It can read the mind of any life form, so Alisa is at first using it on a crocodile at the zoo. Near the end, the children use it to read the mind of the witness and find Kolya in the old house.
Children Are Innocent: When the schoolchildren are looking for Kolya after he was carried away by the pirates, the eyewitness asks "What if [the pirates] have a right to carry boys?" The children reply, as one, "THERE IS NO SUCH RIGHT!" The pirates' torture of Kolya is played much darker than most of their other deeds.
Cold-Blooded Torture: How the pirates plan to extract the location of the Mielofon from Kolya.
Composite Character: Werther is a combination of several future characters from the book.
Computer Voice: The time machine has a computer that speaks in a flat male voice. "Enter the circle. Grasp the handrails. Close your eyes. Breathe deeply. [after trip] Transfer finished. Happy trip!"
Description Porn: The inventory chamber in the Time Institute gives for life forms their species, location, and home era, and for objects their purpose, make, model, producer, and date of production. See here.
Dog Walks You: The big dog that chases Jolly U pulls its owner.
Junior High: School 20. It's in fact a middle school, that is, junior and high combined into one continuous school. Standard operating procedure in the (ex-)USSR.
Medium Awareness: Yulia explains that scientists in the future will name their inventions for the inventions described in science fiction books, showing to Alisa that Kolya Sadovsky is the wrong Kolya.
One Steve Limit: Averted Trope. There are three boys named Kolya in class: Kolya Sulima, Kolya Sadovsky, and Kolya Gerasimov. So Alisa and Yulia come up with The Plan to find the right one.
The Plan: Devised by Alisa and Yulia to find the right Kolya.
Pragmatic Adaptation: Several changes have been made to make the plot more concise, cut down the number of characters, or keep the special effects within the limits of the budget.
Many alien future characters from the book were combined into Werther, who as a biorobot, was easier to film.
Jolly U and Rat were both Starfish Aliens, and only Rat could shapeshift. In the film, both pirates can shapeshift.
The Mielofon is simplified from a box with headphones and wires to a box with a crystal.
Alisa escaped the hospital a day after Yulia did, but in the film both escape on the same day.
The number of scenes of characters arguing has been reduced.
Kolya's last name was Naumov, but had to be changed to Gerasimov because they hired the actor Ilya Naumov (Fima).
Prophecies Are Always Right: Alisa tells the children their futures. However, it's ambiguous if she isn't making this up on the spot.
Harsher in Hindsight: given what we doknow about the kids' future... Wonder if any single one of them survives long enough to see it all and meet Alisa again.
Raygun Gothic: The 2080s, which have energy weapons, space travel, time travel, humanoid robots, flying cars, and the Mielofon. Science and technology are so advanced that schoolchildren regularly launch rockets for projects.
Alisa recalls Alice in Wonderland, except that here it is the boy who falls into the wonderland. Kind of fitting, considering that her name is rendered the same in Russian as that of Lewis Carroll's Alice.