I'm not sure how much Opera can do about it, maybe some.
But what you seeing in the sidebar is basically the same "version of Messenger" that is in www.messenger.com
I haven't used these sidebar messengers - can one change zooming of it's content so that it's no on relation to the main screen? Hmmm try adding custom zoom to setting for www.messenger.com that might work. For the chat heads I don't have an Idea.
