Tomorrow, Alicae is going to school.

Алиса – Alice

Alice in Wonderland :-)

she is going to school for the first time in her life

Truly, already for three months, Alicae herself has been giving no peace to anybody.

The Martian bBooths gave her something amazing, a pencil case, which nobody can open yet, neither me nor my subordinates, including two scientists and main engineer of the zoo.

Boos – Martian's name

ШушаShusha said, «I will go to school together with Alice, checking whether there will be a teacher experienced enough to teach Alicae effectively?

In my memory, when I first went to school, Nnobody made such a fuss about these things.

Now the turmoil had lessenhustle and bustle has died a blittle.

Now hustle and bustle has died a little.

Alicae left for the zoo in order to say goodbye to бронтеяBrontja.

Brontja – his name

For instance, Kate sounds Katja (Катя).

Катя – это реальное имя, а Бронтя – выдуманное. Но правило грамматическое правил составления имени выполнено :-)

AndIn the meantime, when, it got quiet at home, I decided to write some stories about Alicae and her friends’ life.

I will send these stories to Alicae’s teacher.

It will be useful for her to know that she will have to deal with such a frivolous person.

such a mercurial person

I suggest you use word "mercurial" here for the beauty of the translation. This word fits well in the meaning and cosmic context of the story (Mercury).

Probably, these stories will help the teacher to educate my girlto my lovely daughter.

In the beginning, Alisa was a child-likenormal child, until she was three years old.

was a normal child

However, already in one year, when she came across бронтея, Brontja, her ability to do everything inappropriately, toappeared.¶
She disappeared at the most wanted timenecessary moment and toeven discover even accidentallyed by chance things that could not be done by the force of iscovered by the greatest modern scientists, appeared..¶
¶

However, already in one year, when she came across Brontja, her ability to do everything inappropriately, appeared.
She disappeared at the most necessary moment and even discovered by chance things that could not be discovered by the greatest modern scientists.

Alicae can extract benefits for herself from good relationships for herself, but nevertheless she has a lot of true friends.

After all, we cannot stay at home all the time; I work at the zoo, and our motherm constructs houses, also often on other planets.

I want to warn Alisae’s teacher in advance.

Probably, also for her, it will not be easy.

Probably, it will not be easy for her, too.

I let her listen carefully to the absolutely true story, which happened to the girl called Alicae in various places and in space over the past three years.

Tomorrow, Alicasa / Alice is going to school.

It will be an very interesting day.

ASince morning, all her friends and acquaintances has been calleding her on the videophone and congratulateding her.

Truly, alreadyFrankly, for three months, Alica already , Alisa / Alice herself has been giving no peace to anybody.

She has been incessantly talkelling them about her future school.

TBoos, the Martian booth, gave her something an amazing, a pencil case, which nobody canhas been able to open yet, neither me nor my subordinates, including two scientists and main engineercolleagues, among whom there were doctors of science and the chief mechanic of the zoo.

ШушаShusha said, «I willthat he would go to school together with Alice, checking whether there will be a teacher experienced enough to teach Alica effectively?sa / Alice, and check if she got a sufficiently experienced teacher.

It seems you are adding stuff that wasn't there in the original.

Now the turmoil (bustle? commotion?) hads lessened a bit.

Alica left for the zoo in order to say goodbye to бронтеяBrontey / Brontei.

And then, it got quiet at home, I decided to write some stories about Alicasa / Alice and her friends’ life.

I will send these stories to Alica’s teacher.

Check Alisa / Alice everywhere, use just one but consistently.

As a proof of that, I am going to write the first story.

Perhaps, you might want to get it checked by an English native speaker, too

However, already in one year, when she came across бронтея, her ability to do everything inappropriately, to disappear at the most wanted time and to discover even accidentally things that could not be done by the force of the greatest modern scientists, appeared.

Brontei/Brontey

Truly, already for three months, Alicsa herself has been giving no peace to anybody.

I think you should choose only one variant for "Алиса" (you have two: "Alica" and "Alice"). I think the first one is incorrect. The second is okay but I wouls recommend to use a translitaration variant: Alisa.

ШушаSusha said, «I will go to school together with Alice, checking whether there will be a teacher experienced enough to teach Alica effectively?

I think you shouls use "Susha" for "Шуша".