How can I improve my English writing skills, especially letter writing?
Fixed your question first.
The only way to do what you wish, is the same way someone gets to Carnegie Hall, practice, practice, practice.
Get yourself a pen pal and write to them in English. Ask that they correct any mistakes you make in your writing when they send a letter back to you.
You would be able to do this quicker and with less effort if you do it via E-Mail.