(1) is Théorème 7.4.18 of BT1: Bruhat and Tits - Groupes réductifs sur un corps local. Because of (1), to show (2) (as you define it, 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].
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