Corrections in red.  Stylistics in blue.

I want to improve my English.

I want to improve my English. In exchange, I can offer you help with the Russian and Tatar languages. In the evening, I can communicate through my Skype account: Temmi07

I think you were mentally translating подтянуть when you wrote, "I want to pull my English."  If English, you would have to use the phrase "pull up":  "I want to <em>pull up</em> my English."  Such a sentence is fully understandable, but is not 100% natural.  It's better simply to use the word "improve."