1. Bias tape for the borders. Here's a tutorial.
Applique for the designs. A tutorial.
You can probably get by with ironing extra bias tape flat to use with the applique, since her designs are relatively thin.
3. I think cotton sateen (not satin, it's a cotton with a light sheen to it) would look nice. I think you should also use some light/medium weight interfacing for her pennants, to help give them a nice shape. Pleather for her shoes, spandex for the upper portions.