This paper investigates the convergence of a fast-slow stochastic interacting particle system on adaptive networks, where particle states and interaction weights co-evolve, to its nonlinear McKean-Vlasov continuum limit. First, we establish a strong convergence rate for the singular perturbation limit as the relaxation time decrease. Second, we prove the commutativity of the mean-field limit and the fast-adaptation limit. This establishes that the macroscopic dynamics converge to an equivalent effective continuum model regardless of the sequence of the asymptotic approximations. Finally, by introducing a unified pseudo-metric combining the Wasserstein distance and the graphon cut metric, we establish the global empirical stability of the system. This result implies that the macroscopic phenomenological observables and network topology of the system are unconditionally robust against both temporal delays and spatial discretizations, independent of specific microscopic label correspondences. Mathematics Subject Classification (2010). Primary 60K35, 60H10; Secondary 34E15, 05C80