Vacation

In Last month I had a short vacations-- it was only one week. I decided to spend my free time sitting at home. I wanted to just relaxed after my school. I listened to music
, readed books and surfed on the internet.
 During my holiday, I was at home alone, because my boyfriend had to go to work. He has a holiday in another day than I. 
On the first day of my vacation, I cleaned up my flat and then I bought some flowers, to decorate it.
 On the second day of my vacation, I was in Berlin. I needed to take my new passport from the embassy of my country. After that, I took a bus trip across Berlin. I usually like to explore the city by myself. But it was a rainy and cold. Also I didn't have that much time to spend it in Berlin, because I had to catch my bus back to Hamburg in a few hours.

Vacation

In last month I had short vacations, it was only one week. I decided to spend my free time sitting at home. I wanted just relaxed after my School. I listened to music
, readed books and surfed in Internet.
 On my holiday I were at home alone, because my Boyfriend had worked. He has a holiday in another time than I. 
On the first day my vacation I cleaned up my flat und than I boat some flowers, to decorate it.
 On the second day of my vacation I were in Berlin. I needed to take my new passport from embassy of my country. After that I took a bus trip across Berlin. I usually like to explore the city by myself. But it was a rainy and cold. Also I had not so many time to spend it in Berlin, because I had my bus back to Hamburg in a few hours.

I would write like this: 

I decided to spend my free time by relaxing at home after school.

to read/infinitive - read/simple present and simple past

to surf on the internet

On my holiday, ... (comma)

I were... my boyfriend was working

at another time than mine

On the first day, (comma)

I bought some flowers... (no comma after that)

At the second day of my vacation... (comma)

passport from the ambassy...

After that, (comma)

It was rainy and cold 

time to spend in Berlin

becaus there was a bus back...

Overall, you did a great job. You need to pay attention in the comma, preposition choice and verb usage. I hope we can talk and study together. Bye.

Vacation

Last month I had a short vacation, it was only one week. I decided to spend my free time sitting at home, I just wanted to relax after my time at school. I listened to music
, read books and surfed the Internet.
 During my holiday I was at home alone because my boyfriend was working. He has a holiday at a different time than me. 
On the first day of my vacation I cleaned up my flat and then I bought some flowers, to decorate it.
 On the second day of my vacation I was in Berlin as I needed to take my new passport from the embassy of my country. After that I took a bus trip across Berlin. I usually like to explore the city by myself, but it was rainy and cold and I did not have much time to spend in Berlin because I had to catch my bus back to Hamburg in a few hours.