The revolutionary discovery of dark energy and accelerating cosmic expansion was made with just 42 type Ia supernovae (SNe Ia) in 1999. Since then, large synoptic surveys, e.g., Dark Energy Survey (DES), have observed thousands more SNe Ia and the upcoming Rubin Legacy Survey of Space and Time (LSST) and Roman Space Telescope promise to deliver millions in the next decade. This unprecedented data volume can produce the required precision to unambiguously test concordance cosmology which could represent a monumental shift in our understanding of dark energy and its role in cosmic history. However, extracting a pure SN Ia sample with accurate redshifts for such a large dataset will be a challenge. Specifically, spectroscopic classification will not be possible for the vast majority of discovered objects, and only ~25% will have spectroscopic redshifts. This thesis presents a series of observational and methodological studies designed to address the questions associated with this new era of photometric SN Ia cosmology. First, we present a machine learning method for photometric classification of SNe, Supernova Classification with a COnvolutional Neural Network (SCONE). Photometric classification enables SNe with no spectroscopic information to be confidently categorized, and is a critical component of current and future analysis pipelines. SCONE achieves >99% accuracy distinguishing simulated SNe Ia from non-Ia SNe, and has been integrated into DES, LSST, and Roman analysis pipelines. We also demonstrate the efficacy of SCONE on early-time photometric classification, which will be vital for optimal allocation of spectroscopic resources. We show that SCONE can distinguish between 6 SN types with 75% accuracy on the night of initial discovery, comparable to results in the literature for full-phase SNe. Next, we study current methods for estimating SN Ia redshifts and propose a machine learning alternative that uses SN photometry alone to extract redshift information. Most SNe Ia inherit redshift information from their host galaxy, but the process of matching SNe to the correct host galaxy can be challenging. We systematically analyze the impact of incorrect redshifts from host galaxy mismatch on 5 years of DES SN data, and conclude that improved host matching or redshift estimation methods can reduce our systematic errors by ~10%. In response to this finding, we present a SN photometry-only method for estimating redshifts independent of host galaxy information, Photo-zSNthesis. We show that Photo-zSNthesis redshift estimates are accurate to within 2% across the full redshift range of LSST, a first in the literature. Finally, we focus on the robustness of machine learning (ML) algorithms for real-world and scientific applications. ML models generalize poorly beyond their training set and often experience severe performance degradation when deployed on new data. We demonstrate a general method for improving robustness that achieves new state-of-the-art results on astronomical object classification, wildlife identification, and tumor detection.