The action of GT on deformation quantization has been developed in http://arxiv.org/abs/1009.1654 (Willwacher) and before in http://arxiv.org/abs/math/0202039 (Tamarkin).
The fact that GT is Aut(Chain(C2)) is true or not ,depending if you work in the unstable homotopy category (Fresse) Fresse: http://math.univ-lille1.fr/~fresse/E2RationalAutomorphisms.html) or in the stable one (Willwacher). Willwacher: http://arxiv.org/abs/1009.1654).
For new developments concerning the relation between GT and the Galois group of periods of mixed Tate motives over Z, you can take a look at the recent work of Francis Brown.
Damien
