Summary: Based on the recently developed theory of \(\sigma\)-stable sets and stable compactness, we first establish the random Markov-Kakutani fixed point theorem in a random locally convex module: let \((E, \mathcal{P})\) be a random locally convex module and \(G\) be a nonempty stably compact \(L^0\)-convex subset of \(E\), then every commutative family of \(\mathcal{T}_c(\mathcal{P}_{cc})\)-continuous \(L^0\)-affine mappings from \(G\) to \(G\) has a common fixed point, where \(\mathcal{P}_{cc}\) is the \(\sigma\)-stable hull of \(\mathcal{P}\) and \(T_c(\mathcal{P}_{cc})\) is the locally \(L^0\)-convex topology induced by \(\mathcal{P}_{cc}\). Second, we prove that the random Markov-Kakutani fixed point theorem implies the algebraic form of the known random Hahn-Banach theorem. Finally, we establish a more general strict separation theorem in a random locally convex module, which provides not only a more general geometric form of the random Hahn-Banach theorem but also another proof for the random Markov-Kakutani fixed point theorem. Therefore, as a byproduct, the work of this paper also shows that the algebraic and geometric forms of the random Hahn-Banach theorem are equivalent. It should be pointed out that the main challenge in this paper lies in overcoming noncompactness since a stably compact set is generally noncompact.