CutePDF is not an Adobe product, so you should get try to talk to them to see how you can print these elements.
However, chances are that you need to select "Document&Markup" on Reader's print dialog, in order to get these features that you've added in CutePDF.
Karl Heinz Kremer
PDF Acrobatics Without a Net
PDF Software Development, Training and More...
http://www.khkonsulting.com