The Zwicky Transient Facility SN Ia Data Release 2 (ZTF SN Ia DR2) contains more than 3000 Type Ia supernovae (SNe Ia), providing the largest homogeneous low-redshift sample of SNe Ia. Having at least one spectrum per event, this data collection is ideal for large-scale statistical studies of the photometric, spectroscopic and host-galaxy properties of SNe Ia, particularly of the more rare 'peculiar' subclasses. In this paper, we first present the method we developed to spectroscopically classify the SNe in the sample, and the techniques we used to model their multi-band light curves and explore their photometric properties. We then show a method to distinguish between the 'peculiar' subtypes and the normal SNe Ia. We also explore the properties of their host galaxies and estimate their relative rates, focusing on the 'peculiar' subtypes and their connection to the cosmologically useful SNe Ia. Finally, we discuss the implications of our study with respect to the progenitor systems of the 'peculiar' SN Ia events.