I am very happy

Saturday was a very great day for me. I went to a shop in my city and i I bought the a ticket to the concert of my favourite italian singer and rapper, J Ax. On 4 September i I will go to the concert with my best friend and i am sure that it will be amazing.
I have loved this singer since 2005, when i met for the first time the girl who became my best friend for ther first time.

("for the first time" sounds much better at the end of a sentence, though the way you wrote it is OK)

I listened to rap music, but i didn't know this rapper and when we talked about music, she say said some things about him and i immediately listened his songs.
I don't know if you know who he is, but i recommend urge you to read the text of his songs..and really you appreciate him.

(recommend is very difficult to use with a verb in English - it usually sounds very clumsy.  It's normally used with a noun...

 I recommend the pasta, or I recommend swimming, or I recommend a visit to Lucca, but I urge you to listen or I urge you to try again, or I urge you to sing that song to me)

I hope this text is better than others...;)
xoxo
Jess

I think your English is really good - my corrections are mostly ways of sounding more natural rather than correcting errors.  Although we *always* write 'I' as a capital letter!