A few more corrections in red, and a few stylistic suggestions and variants in blue:

So, I'm the member of a scanlaters team named/called Silver Stone Studio. In this team I'm a translator from English to Russian, and now I'm working on manga named Hatsukoi Monster by HIYOSHIMARU Akira.

But anyway, this manga is loved by a lot of people, to be exact, by teenage girls. Besides English, I'm learning Japanese. But in Japanese I'm not even on a beginner/beginner's/beginning level. Now I'm learning Hiragana, and I'd never [1] imagined that it could be so interesting. 

I'll do my best to become a polyglot.

[1]  The present perfect would be correct if you haven't imagined it until the present moment.  However, it is clear from the context that at the present moment you are fully aware of how interesting Hiragana is.  So use the past perfect instead. 

I made only two corrections.

First: 

I've been learning English for 8-9 years at my school. And I'm also learning English by myself at home.

or we can say this:

I've been learning English for 8-9 years at my school, and I'm also learning English by myself at home.

The coordinating conjunctions are and, but, for, nor, or, so, and yet. We can't start a sentence with one of these conjunctions. Either you can use it to connect two linking sentences, or you can begin the sentence without and.

Second: 

Besides English, I'm learning Japanese. But in Japanese I'm not even on a Beginner level.

Use commas to set off transitional words -such as however, therefore, moreover, or besides- from the rest of the sentence.

Please, correct my mistakes.

Hi, there! My name Is Julia and I'm from Russia. I've been learning English for 8-9 years at my school. And I'm also learning English by myself at home. I enjoy it a lot! I'm totally in love with English and Japanese modern culture. So I'm the member of a scanlaters team names Silver Stone Studio. In this team I'm a translator from English to Russian and now I'm working at manga named Hatsukoi Monster by HIYOSHIMARU Akira. This manga is so cute and... strange. But anyway, this manga is loved by a lot of people, exactly by teenager girls. Besides English I'm learning Japanese. But in Japanese I'm not even on a Beginner level. Now I'm learning Hiragana and I've never imagined that it could be so interesting.
I'll do my best in becoming a polyglot.