Is my spanish correct in this letter?

porque is because. Por que is why. That was the only thing wrong in the very beginning. And i dont know if it matters to you but if you want to say i will write more letters you could use " Escribire mas cartas" or you can leave it as i am going to write more letters which you have since you used voy a escribir.. but either way it works. And i think you are okay using the tu form