Прошу проверить мое письмо, хочу отправить англичанке)

Good job, Tararam! :) A few corrections/suggestions:

Hello, my kind friend! (Sure, you are kind, because I hope that you will like my letter.)
This is the first time that I am writing such an unusual letter not in my native language. My name is Nadya and, perhaps, you’ve already guessed that I’m from Russia. I live in a small but the most beautiful town Dergachi. I’m 13 and I am in 7th grade. I love to read. I am actively studying English, because I really like this subject. I’m keen on tennis. I like intellectual games and humorous competitions. My friends say that I am kind and funny. What more can I tell you?.. I don’t know. Maybe I’ll keep some secrets about myself so you'll get to know me better in the next letter (I hope it will be so?). Generally, I love many things in my life.
So, as I have already told you, I really enjoy reading. Now I am reading a trilogy by William Nicholson. It's fantastic! I like to watch horror movies and anime. My favorites are Naruto, Mirrors, Sillent Hill, Beck. I like to read Russian classics very much: Pushkin, Gogol and Block. They are known by the whole world for their great literary work.
Unfortunately I still don't speak English very well, but I learn every day and I hope that I will speak better soon. Don't laugh if I made any mistakes.
I am eager to find out more about you, to ask you about everything that you find interesting.
Well, so long my kind friend!

I am active at learning of English
Don't laugh, if I made some mistakes.

Learning English (без оф)
Лучше слово plays заменить на games
Any more имеет немного другой смысл (чаще в отрицательных предложениях) , здесь лучше поставить что-нибудь типа else
FROM the next letter? По-моему, по смыслу больше подходит in
I like watching (т. к. говорится о личных предпочтениях)
Не I could, а I will вe aвle (could - это прошедшее время)
Ну и если пишешь именно англичанке, а не американке, то лучше замени movies на films, grade на form ;)