Hello, my name is Laura. I'm 18 years old. This is the first time I that I have written write in English in this page [website]. I want to learn English in this summer because I would like to study in England the next year. Now I'm studying in Madrid. I just finished school and I'm preparing for my test to enter in university entrance exam. I'm very busy.
     I study music too. I'm musician an oboist and I study music in at a professional conservatory in Madrid. In the future, I would like to travel around the world to know learn about [to be exposed to] the different types of music, and I want would also like to meet a lot of the musicians who compose and perform them. 

Laura,
"That I have written" replaces "that I write."
We write "on the page," not "in the page."
"Just finished" is the past-tense of "I finish." This happened in the past.
We know that you are a musician. You said "I study music," so it is good to write "I am an Oboist."
We must learn about the music before we know the music.
We started the sentence with "I would like to" so lets stay with the subjunctive and repeat "I would also like to. . ." 
Very good. Feel free to reply if I am not clear, y escríbame si no entiende. 
--Dan 

Introduction

Hello, my name is Laura. I´m 18 years old. This is the first time I write in English on this site.
I want to learn English this summer because I would like to study in England next year. I just finished school and I´m preparing myself for my entrance test to university in Madrid. I´m very busy. I study music, too. I´m a musician (oboist) and I'm studying music in a professional conservatory in Madrid. In the future, I would like to travel around the world to know about the different types of music and I want to meet a lot of international musicians. That's all for today, bye! :)