The English is very good, just one or two little suggestions for minor corrections.
It would make it more fluid and readable in English without the "with" in the first phrase. Taking out "to" before the two verbs would be good too. I think a comma between "things" and "together" helps too.
Then the phrase would read:
Hello, I really want to meet you, make friends and share some things, together with people from different cultures.
Let me know what you think, and we'll edit. Ive set a poll as I don't speak any Turkish.
kafetzou's suggestion conveys the meaning better especially after the comma "become friends and share some things as people from different cultures."
There isn't any problem with the part before the comma.
Netcevap I'm awfully sorry but in the correction that you suggest there are two flaws "being friend, I want share some .." firstly "being friend" doesn't mean anything in English "being friendly" maybe. Secondly, "I want share some" the verb "share" is used here in it's infinitive form and needs "to" before it => "to share".