Type Ia supernovae are remarkable for their use as distance indicators, yet a coherent physical explosion mechanism continues to elude us. In this talk, I will discuss my dissertation, which addresses many areas of contemporary SN Ia physics. I present a new light curve fitting technique, called "2-stretch", which demonstrates the diversity in SN Ia light curve shapes. 2-stretch also has implications when estimating the amount of nickel-56 produced in the explosion, which powers the light curve through radioactive decay. I will present a direct search for SN Ia companion stars. Using the SDSS-II dataset, I am able to constrain possible progenitor models in the single degenerate channel, where a type Ia supernova reaches the critical Chandrasekhar limit by accretion of material from a non-degenerate companion star. This work confidently rules out red giants near Roche-Lobe overflow as common companions to type Ia supernovae. Lastly, I address one of the most pressing current topics in SN Ia cosmology, the correlation of SN Ia distances with host galaxy parameters. I apply the Fundamental Metallicity Relation (FMR) of Mannucci 2010 to SN Ia host galaxies and find that the Hubble residual correlation with galaxy properties is consistent with the FMR.