We study the processes γγ → η ′ K + K − , η ′ π + π − , and ηπ + π − using a data sample of 519 f b −1 recorded with the BaBar detector operating at the SLAC PEP-II asymmetric-energy e + e − collider at center-of-mass energies at and near the Υ(nS) (n = 2, 3, 4) resonances. This is the first observation of the decay η c → η ′ K + K − and we measure the branching ratio Γ(η c → η ′ K + K − )/(Γ(η c → η ′ π + π − ) = 0.644 ± 0.039 stat ± 0.032 sys . Significant interference is observed between γγ → η c → ηπ + π − and the non-resonant two-photon process γγ → ηπ + π − . A Dalitz plot analysis is performed of η c → η ′ K + K − , η ′ π + π − , and ηπ + π − . Combined with our previous analysis of η c → K K̄π, we measure the K 0 ∗ (1430) parameters and the ratio between its η ′ K and πK couplings. The decay η c → η ′ π + π − is dominated by the f 0 (2100) resonance, also observed in J/ψ radiative decays. A new a 0 (1700) resonance is observed in the η c → ηπ + π − channel. We also compare η c decays to η and η ′ final states in association with scalar mesons as they relate to the identification of the scalar glueball.