In this study, we explore the characteristics of ‘low-mass’ (log(M⋆/M⊙) ≤ 8) and ‘intermediate-mass’ (8 < log(M⋆/M⊙) ≤ 10) host galaxies of Type Ia supernovae (SNe Ia) from the second data release (DR2) of the Zwicky Transient Facility survey. We investigated their correlations with different sub-types of SNe Ia. We used the photospheric velocities measured from the Si IIλ6355 feature, SALT2 light-curve stretch (x1), and host-galaxy properties of SNe Ia to re-investigate the existing relationship between host galaxy mass and Si IIλ6355 velocities. We also investigated sub-type preferences for host populations. We show that the more energetic and brighter 91T-like SNe Ia tend to reside among the younger host populations, while 91bg-like SNe Ia are found among the older populations. Our findings suggest that high-velocity SNe Ia (HV SNe Ia) do indeed come from older populations, but they can also come from young populations as well. Therefore, while our findings can partly provide support for HV SNe Ia in the context of single degenerate progenitor models, they indicate that HV SNe Ia (rather than comprising a different population) might be a continued distribution with different explosion mechanisms. Lastly, we investigate the specific rate of SNe Ia in the volume-limited SN Ia sample of DR2 and compare our results with other surveys.