Good corrections by Graham :) Here are some others:

I writer am writing a letter to my cousin Luisa.

Dear cousin Marisa,

How are you? what's the weather over there? For here It's very sunny.

I'm writting writing to you because my teacher ask me homework , I have writting a letter or mail to someone.

I'm doing explain how he is. Your name is James. He is very tall and thin. James's hair is brown. He is forty-seven yeart old more or less. He is a good comunicator communicator, he is very expresive expressive. He's brother's my boss.
He must laugh a lot because I Have a very basic level English, especially when I speak.

I'm doing the english cours en my work with my partners. <-- Are you trying to say that you are doing your English course homework with your classmates?

I hope to see you soon.

Regards to my uncles, too.

I writer a letter to my cousin Luisa.

Dear cousin Marisa,

How are you? what's the weather like over there?  It's very sunny here. 

I'm writting to you as my teacher asked for our homework assignment, that we write a letter or email to someone.

I'm going explain what he is like. His name is James, he is very tall and thin. James' hair is brown. He is about forty-seven years old. He is a good comunicator , he is very expresive. His brother's my boss. 

He must laugh a lot because my English is very basic, especially when I speak.

??? Unsure what you are trying to say here ??? 

I hope to see you soon.

Give my regards to my uncles, too.