Evolution of low- and intermediate-mass stars with [Fe/H] <= - 2.5

We present extensive sets of stellar models for ranges 0.8-9.0 M_solar in mass and -5 <= [Fe/H] <= - 2 and Z = 0 in metallicity. The present work focuses on the evolutionary characteristics of hydrogen mixing into the helium-flash convective zones during the core and shell helium flashes that occur for models with [Fe/H] <~ - 2.5. Evolution is followed from the zero-age main sequence to the thermally pulsating asymptotic giant branch (AGB) phase, including hydrogen engulfment by helium-flash convection during the red giant branch (RGB) or AGB phases. Various types of mixing episodes exist, with regard to how hydrogen mixing sets in and how it affects the final abundances at the surface. In particular, we find hydrogen ingestion events without dredge-ups that enable repeated neutron-capture nucleosynthesis in the helium-flash convective zones with ¹³ C (α, n)¹⁶ O as the neutron source. For Z = 0, the mixing and dredge-up processes vary with the initial mass, which results in different final abundances at the surface. We investigate the occurrence of such events for various initial mass and metallicity values to find the metallicity dependence for helium-flash-driven deep mixing (He-FDDM) and also for third dredge-up events. In our models, we find He-FDDM for M <= 3 M_solar for Z = 0 and for M <~ 2 M_solar for -5 <= [Fe/H] <= - 3. However, the occurrence of the third dredge-up is limited to the mass range ~ 1.5-5 M_solar for [Fe/H] = - 3, a range that narrows with decreasing metallicity. This work also discusses the implications of the results of model computations for observations. We compare the abundance pattern of CNO abundances with that for observed metal-poor stars. The origins of the most iron-deficient stars are discussed by assuming that these stars are affected by binary mass transfer. We also point out the existence of a blue horizontal branch for -4 <~ [Fe/H] <~ - 2.5.