(1) is Théorème 7.4.18 of [BT1: Bruhat and Tits - Groupes réductifs sur un corps local](http://www.numdam.org/item?id=PMIHES_1972__41__5_0).  Because of (1), to show (2) (as you [define it](https://mathoverflow.net/questions/431445/does-an-affine-building-associated-to-a-group-satisfy-the-axioms-of-building/431467#comment1110480_431445), i.e., transitivity of the action of $G$ on apartment–chamber pairs) it suffices to show that the stabiliser of a chamber acts transitively on the apartments containing that chamber.  This is Corollaire 7.4.9(i) of [BT1].