Hello, and welcome from Idaho!
1. You can string quilt on paper and then tear the paper away. You can also string quilt on a foundation such as cheap musling or worn out sheets. I would guess that she was using adding machine tape to keep it straight and reduce the chances of stretching the fabric.
2. Paper piecing is usually used when making difficult patterns that would be hard to cut out. You sew the fabric on the paper pattern and tear the paper away when you are finished.
3. The directions that are given in the pictures area are pretty easy to understand. If you read through and don't understand ask.