Well, first of all, I'm happy you liked this story! And then, never apologize for a long comment! Seriously, authors love long comments. It shows that you really did pay attention to the story and were willing to sacrifice a few minutes to tell the author you liked it. That means a lot. The fact that you are struggling with the English language (though I wouldn't have been able to tell, your English is really good) makes me appreciate it even more.

To answer your question: Yes, the conditions of Dean's surrender are mentioned in the sequel somewhere, though that story is so long I don't blame you for not remembering. The conditions were this: He wanted Michael to kill Sam for good and make sure he couldn't be resurrected so Lucifer could never take over. So Michael burned Sam alive before Dean's eyes and then put Dean's consionsness to sleep before Sam came back to life, so Dean would never know Michael lied to him.