1.Yvain gains a new identity known as the knight and the lion, Why does he need a new identity?

Yvain starts to refer to himself as the "knight with the lion." Yvain's new name is a declaration of his new life. He now sees that he can redeem himself and start better than he was before; quite similar to Erec, is rebirthed after the fight with the lion and the snake. In choosing the life with the lion, Yvain chooses to be a better knight. Rather than fight for all his own glory, he wants to fight and be chivalric simply because he sees it is the better way to live.

3. Yvain and Laudine meet again at the end, What kind of reconciliation is this then?

At the end of the text, Yvain and Laudine do in fact end up together. Rather than having the mood be a mutual feeling of profound love and romance, I got the impression it was more of a business transaction for Laudine. She does not want to be accused and have her reputation spoiled. In return, Yvain's apology and profession of love seems un-reciprocated. He pours his heart out to her and she simply accepts it and sees the other benefits of reuniting.