We report the measurements of gamma gamma ―> eta_c(1S), eta_c(2S)―>eta' pi+ pi- with eta' decay to gamma rho and eta pi+ pi- First observation of eta_c(2S)―>eta' pi+ pi- with a significance 5.5 \sigma including systematic error is obtained. The products of the two-photon decay width and branching fraction of decays to eta' pi+ pi- are determined for the eta_c(1S) and eta_c(2S), respectively. A new decay mode for the eta_c(1S)―>eta' f0(2080) with f0(2080)―>pi+ pi- is observed with a statistical significance of 20 \sigma. The cross section for gamma gamma ―> eta' pi+ pi- and eta’ f2(1270) are measured for the first time. We also report a measurement of the cross section for K^0_S pair production in single-tag two-photon collisions, gamma gamma → K^0_S K^0_S for Q^2 up to 30 GeV^2, where Q^2 is the negative of the invariant mass squared of the tagged photon. The measurement covers the kinematic range 1.0 GeV < W < 2.6 GeV and |cos theta|<1.0 for the total energy and kaon scattering angle, respectively, in the gamma* gamma center-of-mass system. For the first time, the transition form factor of the f'2(1525) meson is measured separately for the helicity-0, -1, and -2 components and also compared with theoretical calculations. Finally, the partial decay widths of the chi_c0 and chi_c2 mesons are measured as a function of Q^2. The results are based on a data sample collected with the Belle detector at the KEKB asymmetric-energy e+ e- collider.