  We present extensive sets of stellar models for 0.8-9.0Msun 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 He-flash convective
zones during the core and shell He flashes which occurs for the models with
[Fe/H] <~ -2.5. Evolution is followed from the zero age MS to the TPAGB phase
including the hydrogen engulfment by the He-flash convection during the RGB or
AGB phase. There exist various types of mixing episodes of how the H mixing
sets in and how it affects the final abundances at the surface. In particular,
we find H ingestion events without dredge-ups that enables repeated
neutron-capture nucleosynthesis in the He flash convective zones with 13
C(a,n)16 O as neutron source. For Z = 0, the mixing and dredge-up processes
vary with the initial mass, which results in different final abundances in the
surface. We investigate the occurrence of these events for various initial mass
and metallicity to find the metallicity dependence for the He-flash driven deep
mixing (He-FDDM) and also for the third dredge-up (TDU) events. In our models,
we find He-FDDM for M <= 3Msun for Z = 0 and for M <~ 2Msun for -5 <~ [Fe/H] <~
-3. On the other hand, the occurrence of the TDU is limited to the mass range
of ~1.5Msun to ~5Msun for [Fe/H] = -3, which narrows with decreasing
metallicity. The paper also discusses the implications of the results of model
computations for observations. We compared the abundance pattern of CNO
abundances with observed metal-poor stars. The origins of 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.
