Translation - Turkish-English - eğer benimle çıkarsan, gördüğüm ilk ejderhayı...

"to go out with/to date" are better choices for "çıkmak"

I don't see a big difference. As a result one wants to be friends with someone.

"çıkmak" has several meanings but "to become a friend" is not one of them merdogan. If you do not want to involve a relationship in the meaning, then use "to go out".

I don't agree with you .
If it dosen't mean "to become a friend" who can kill a dragon for someone?

If you date me, I will kill the first dragon I see for you.