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 rarer peculiar'sub-classes. 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 sub-types and the normal SNe Ia. We also explore the properties of their host galaxies and estimate their relative rates, focusing on the peculiar sub-types 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.