Those garments are made of silk, and the pattern is woven, not dyed or embroidered. Usually for members of the royal family the rondels would have a stylised depiction of a sixteen-petalled chrysanthemum, but I can't see it closely enough to be sure what the design is.
I'm not really sure about the formal kimono, because the article says that girls wear a skirt called a mo whereas boys wear baggy trousers called hakama; however, from what I understand, the mo is a train which is worn at the back over several layers of kimono, all of which are worn over hakama by women as well as men.
If you look at the pictures on these pages
http://www.clotheslinejournal.com/heian.html
http://www.nijo.co.jp/coupon/p23.htm
the mo is the white train at the back, and you can see the red trousers under all the layers of robes.
These days, as a result of sumptuary laws, the formal outfit (called juni hitoe, which means twelve layers) is a maximum of five layers, although it doesn't look as though Aiko is wearing that many. The different colour combinations for the layers are dependent on the season and the social class of the person.
I'm not sure what the pink coat is about; it may just be a less formal robe to wear over the hakama once the formal layers were removed. The long sleeves, which nearly reach the ground, are worn by children and unmarried women. If you look at photos of Empress Michiko in kimono, her sleeves are a lot less voluminous, which is the way married and older women wear them.