Studying the origins of the high-energy emission in the Universe can profoundly affect our fundamental understanding of the cosmic origin and its evolution at the most extreme scales. In this dissertation, I explore the high-energy observations of different astrophysical systems to inform our understanding of the theoretical frameworks used to describe them. I harness the current multimessenger infrastructure to investigate questions ranging from new physics and transient astronomy to compact objects and extended emission in the gamma-ray, gravitational-wave, and neutrino skies.

The focus in the first part of this dissertation is on utilizing the Fermi Large Area Telescope (LAT) low-energy (LLE) technique to search for the light axion-like-particle (ALP) within the MeV gamma-ray emission of long gamma-ray bursts (GRBs). We perform a data-driven sensitivity analysis to determine distances for which detection of an ALP signal is possible with the LLE technique, which, in contrast to the standard LAT analysis, allows for a larger effective area for energies down to 30 MeV. Assuming an ALP mass $m_a \lesssim 10^{-10}$~eV and ALP-photon coupling $g_{a\gamma} = 5.3\times 10^{-12}$ GeV$^{-1}$, we find that the distance limit ranges from $\sim!0.5$ to $\sim!10$~Mpc. We demonstrate that the sensitivity of the LLE technique to detecting light ALPs is comparable to the standard LAT analysis, making it an excellent complementary---yet independent---way to search for ALPs with \textit{Fermi}.

Next, we select a candidate sample of twenty-four GRBs and conduct a model comparison analysis in which we consider different GRB spectral models with and without an ALP signal component. We find that including an ALP contribution does not result in any statistically significant improvement of the fits to the data. Motivated by the delay between the ALP emission time and the time of the jet break-out associated with its ordinary long-GRB emission, we conduct a novel search for ALPs within time windows that precede the main-episode gamma-ray emission of a long GRB, focusing on the sample of sources with known precursor emission detected with LAT and LLE. We report no statistically significant detection of ALPs within the GRB precursor emission and discuss the parts of the ALP parameter space probed with this method.

Multimessenger astronomy is at the heart of the remainder of this dissertation. First, I present a follow-up search for excess emission of X-rays with the Swift Burst Alert Telescope (Swift-BAT) and that of gamma rays with the Fermi Gamma-ray Burst Monitor (Fermi-GBM), in spatial and temporal correspondence to gravitational-wave events reported by the LIGO/Virgo/Kagra (LVK) Collaboration. In collaboration with the Fermi-GBM Team, we combine the observations from these two instruments to determine whether there is any statistically significant excess emission around the given gravitational-wave trigger. We report no new joint detections but present the joint flux upper limits.

Finally, I present the results of the cross-correlation studies between the unresolved Fermi-LAT gamma-ray and the IceCube neutrino skies. We report no positive cross-correlation in the real-data sky maps. We then combine simulation and observation techniques to place upper limits on the fraction of neutrinos produced in proton-proton or proton-gamma interactions that occur in blazars. Assuming all gamma rays from unresolved blazars are produced from neutral pions via proton-proton interactions, we find that---for energies above 10~GeV---up to 60 % of the unresolved blazar population may contribute to the diffuse neutrino background (the fraction is 30 % for proton-gamma interactions). We also include predictions for the improved sensitivity considering 20 years of IceCube data.