This thesis investigates anomalous Higgs boson couplings and effective field theory (EFT), focusing on their implications for Higgs boson production and decay processes. The work includes contributions to significant phenomenological studies, including Monte Carlo simulation and matrix element libraries for data analysis, emphasizing the analysis of H → 4 lepton decays. A major component of the research is the innovative approach to gamma + H production driven by EFT operators, which facilitates the use of on-shell Higgs production and H → 4 lepton decay to constrain light quark Yukawa couplings in the first two generations. The thesis culminates in results highlighting EFT and polarization measurements in H → ZZ utilizing combined Run 2 and Run 3 LHC data. The polarization measurements establish quantum entanglement in the ZZ system and have implications for tests of Bell-type inequalities. Additionally, the thesis covers developments in the Silicon Tracker project, emphasizing key contributions to alignment efforts.