1. There was only a hour of the boardcast so you can only insert so many songs in the boardcast. Maybe it was figure out that Elvis did the post songs on stage without a audience so they could insert them into the show since they have time.
2. Parker wasn't there illegally at all. He was still in the USA. You don't have to have a passport to go to Hawaii since it is a state. It is like Colonel Parker could have Elvis go to Puerto Rico since it is a territory of the US. You don't need a passport to go to Hawaii or the territories that US has.