[en] Proximity-induced magnetic effects on the surface Dirac spectra of topological insulators are investigated by scanning tunneling spectroscopic studies of bilayer structures consisting of undoped Bi₂Se₃ thin films on top of Cr-doped Bi₂Se₃ layers. For thickness of the top Bi₂Se₃ layer equal to or smaller than 3 quintuple layers, a spatially inhomogeneous surface spectral gap Δ opens up below a characteristic temperature ${T_{\mathrm{c}}}^{2\mathrm{D}},$ which is much higher than the bulk Curie temperature ${T_{\mathrm{c}}}^{3\mathrm{D}}$ determined from the anomalous Hall resistance. The mean value and spatial homogeneity of the gap Δ generally increase with increasing c-axis magnetic field (H) and increasing Cr doping level (x), suggesting that the physical origin of this surface gap is associated with proximity-induced c-axis ferromagnetism. On the other hand, the temperature (T) dependence of Δ is non-monotonic, showing initial increase below ${T_{\mathrm{c}}}^{2\mathrm{D}},$ which is followed by a ‘dip’ and then rises again, reaching maximum at T ≪ ${T_{\mathrm{c}}}^{3\mathrm{D}}.$ These phenomena may be attributed to proximity magnetism induced by two types of contributions with different temperature dependences: a three-dimensional contribution from the bulk magnetism that dominates at low T, and a two-dimensional contribution associated with the RKKY interactions mediated by surface Dirac fermions, which dominates at ${T_{\mathrm{c}}}^{3\mathrm{D}}$ ≪ T < ${T_{\mathrm{c}}}^{2\mathrm{D}}.$ In addition to the observed proximity magnetism, spatially localized sharp resonant spectra are found along the boundaries of gapped and gapless regions. These spectral resonances are long-lived at H = 0, with their occurrences being most prominent near ${T_{\mathrm{c}}}^{2\mathrm{D}}$ and becoming suppressed under strong c-axis magnetic fields. We attribute these phenomena to magnetic impurity-induced topological defects in the spin texture of surface Dirac fermions, with the magnetic impurities being isolated Cr impurities distributed near the interface of the bilayer system. The long-term stability of these topologically protected two-level states may find potential applications to quantum information technology. (paper)