Why am I learning English?

***You have to capitalize I

I've been learning English for about a month but I was learning it at the school at the my university.

***I'm = I am, which is present tense.  But you're speaking about an unfinished action, which is present perfect progressive tense.

***Your second sentence repeats most of the first - it is simpler to join them.

 It wasn't a good experience, because school teachers always changed quit and we didn't educate practice enough grammar or speaking.

***Change is a word with several meanings.  Saying "the teacher changed" is like saying перемена к лучшему; quit refers to the teacher quitting her job.

***A teacher educates you, but you do not educate yourself.  You learn, or practice grammar/speaking.

My nearest purposegoal is take the KET. Then I'm going to take the PET and take the PET next year. It's like a challenge for me. Most important skill My weakest skill in English education for me is speaking. When I've improved this skill to good level, i could I will be able to speak to foreigners. 

***There's a word for this - goal.

***Speaking is the most important skill for you to practice because it is your weakest skill, but it is not the most important skill overall.

***You can just say English - it's clear that you are referring to the language.

***I'll = I will, which is future tense.  Even though your goal of speaking is in the future, it is an action started in the past which continues through the present.  So for this, again, you use present perfect progressive.

***You can just say "When I've improved" - the context is clear (your speaking skill), as is the goal (to a good level).

***You can't speak to foreigners now, but you WILL be able to in the future.

Maybe, I'll change my job or I'll decided to move to another city, I don't know. But I don't want to leave my country. This is my homeland and there was buried my mother my mother is buried here.

***I'll is repeated - you only need to say it once, before listing things.

***Decided is past tense.

***Because you are in Russia now, Russia is HERE, not THERE.

***Though your mother WAS buried, she still IS buried.  So you use present tense.

Anyway, I knew learned many interesting things during last month. My education is becoming more and more exciting!

***учить, not знать

***You can just say last month.

***I know you just misspelled this, but exiting is to leave a building :)

***Very good!