I have a important exam afterin a month, so I practice English in the school.

But the, studying for the exam is boreding.

Most of sentences I reoad are about someone's peaceful daily life.

Thus, I want to learn English with sentences read inwritten about the real world.

I have an important exam afterin a month, so I practice English in theat school.

I understand what you're saying, the corrections just make it sound more like it's coming from a native speaker.

But the studying for the exam is boreding.

Most of the sentences I read are about someone's peaceful daily life.

(I didn't change "peaceful", but it seems like you probably meant something like "monotonous" instead)

ThusSo, I want to learn English with sentences read in the real world.

"Thus" works, and personally I love "thus", but you don't hear it very often in everyday English anymore. It might be used in a really formal setting (like a courtroom), or perhaps a movie.

I have an important exam afterin a month, so I practice English in theat school.

Use 'an' before words that start with a vowel.
--> a cat, a dog, a book BUT an idea, an event, an important exam

When you want to say something will happen after a period of time, say 'in'.
--> I have a test in two days. We have a meeting in an hour. We'll get married in a year.

Use 'at' when describing the location where you do something.
--> I cook at home. I study at school. I read at the library.

But the studying for the exam is boreding.

"Studying' instead of 'the study' because you're describing the process of studying as boring. 'A study' actually means a research paper.

Say 'the exam' because you are referring to a specific exam in the future and not just in general. Not putting any article or possessive pronoun before your noun is grammatically incorrect.
--> I'm studying for the exam OR I'm studying for my exam (there's a specific exam I'm studying for)

'Boring' is an adjective to describe something. 'Bored' is to describe how you're feeling.
--> I'm bored with studying (you feel bored) OR Studying is boring.6

Most of the sentences I read are about someone's peaceful daily life.

Remember to put articles before your nouns.

I have a important exam afterin a month's time, so I'm practiceing English in theat school.

Instead of "in a month's time" you could also use "a month from now"

But the studying for the exam is boreding.

"bored" describes a state of being, while "boring" describes what makes you bored.

I'm indifferent to them.

"I'm indifferent" can sound somewhat neutral - based on what you wrote in Japanese you could strengthen this to emphasise how much you do not care about them.
"I have no interest in them." gives a stronger impression of not caring.