Type Ia supernovae are excellent distance indicators for cosmology due to their extreme and predictable luminosities. Of particular interest is the use of type Ia supernovae as standard candles to calculate the Hubble constant. The Hubble constant describes the current expansion rate of the universe, and depending on the method used to calculate it, the value can vary between 67 and 75 km/s/Mpc. The difference in Hubble constant values could indicate that there is new physics yet to be discovered, but it could also come from a much simpler source -- an incomplete understanding of the observations and the systematic uncertainties involved. Overall, my thesis aims to understand type Ia supernovae, their intrinsic variations, and if those variations have any effect on the measurement of the Hubble constant.The first project in my thesis focuses on distinguishing between progenitor systems for individual type Ia supernova events. These supernovae could come from a single-degenerate system, where a white dwarf accretes material from a companion star, or a double-degenerate system, where two white dwarf stars merge. The single-degenerate scenario is expected to create more dust in the immediate vicinity of the explosion. I look for evidence of such nearby dust through light echoes. Light echoes provide several advantages over other methods for searching for dust, mainly because they are observable for much longer time scales. In particular, I look at SN 2009ig, a relatively normal type Ia supernova in the face-on spiral galaxy NGC 1015. Using ground-based observations from the Large Binocular Telescope and the Kitt Peak National Observatory, I construct the late-time light curve of SN 2009ig and show that it deviates from the expected light curve behavior starting around 700 days post-peak. This deviation suggests that a light echo is present, which I confirm through archival Hubble Space Telescope imaging. The archival imaging shows that the light echo has a complex structure, suggesting that the local dust environment is quite clumpy. However, I am not able to distinguish if SN 2009ig resulted from a single-degenerate system with the available data. The second project in my thesis focuses on the correlations between type Ia supernova properties and their host galaxy properties. Using surface brightness fluctuations to measure the distances to 25 type Ia supernovae in elliptical galaxies, I can compare how the properties of type Ia supernovae in elliptical galaxies compare to those in spiral galaxies with distances measured by Cepheid variables. I find that the supernovae in elliptical galaxies tend to be dimmer and faster declining, and they occur in much more massive host galaxies. Additionally, I can recalculate the value of the Hubble constant using a set of supernovae that are the most dissimilar to those calibrated by Cepheids to test if the difference in supernovae properties has any effect on the Hubble constant. Using a Markov Chain Monte Carlo simulation to re-fit the calibration parameters to these faster declining supernovae in much more massive hosts, I find that the value of the Hubble constant is statistically indistinguishable from results using Cepheid distances. Therefore, I conclude that type Ia supernova variations are not the solution to the Hubble constant tension.