Opera 12 had this. The one thing I didn't like about it though is that all private tabs in a windows shared the same session. Would rather have each private tab have its own session where links opened in a new tab from a private tab share the session of their parent private tab.
1: Sync is not yet available
So use a version of Opera that supports Sync. The beta release (Opera 28) has basic support for it. The Development release (Opera 29) also has it.
2: UI wise - The opera button in the top left should be positioned like a tab imo.
I don't know what you mean.