To do a cookie box is pretty straightforward -- let's take her example of a paisley cutter. Cut two cookies from the paisley cutter. Then cut a 1 inch strip and make it long enough to curve around the outside of the cutter. Place on top of one of the uncooked cookies and glue with water (leaving the cutter inside. Bake all cookies. Now you have a "box" and a cookie for a lid.
As for her piping, it looks like pattern transfer to me using royal icing with a teeny tiny tip (maybe a 1 or smaller.)
You're right, she does amazing work!!
Hope that helps some.