The FASER Collaboration has updated simulations and presented theoretical predictions for neutrino fluxes and cross sections, along with their uncertainties, to support future neutrino measurements at the LHC. FASER, located 480 m from the ATLAS interaction point, has detected collider neutrinos for the first time, with 153 muon neutrinos observed in 2022. The experiment is expected to collect 250 fb⁻¹ in LHC Run 3 and 930 fb⁻¹ in Run 3 + Run 4. These neutrino event rates, along with their energy and spatial distributions, will enable studies of neutrino scattering cross sections, forward hadron fluxes, parton distribution functions, and new physics. Neutrino fluxes are primarily produced by the weak decay of light and charm hadrons. The fast neutrino flux simulation, based on Monte Carlo event generators, has been updated for LHC Run 3 and Run 4 configurations. The simulation accounts for beam crossing angles, magnetic fields, and hadron production. The neutrino flux is estimated using the fast neutrino flux simulation, validated against full simulations. The flux uncertainties are mainly due to hadron production modeling, while interaction cross sections are modeled using the Bodek-Yang model and newer NLO structure function models. These models are compared, and cross-section uncertainties are defined. The neutrino event rates for electron, muon, and tau neutrinos are predicted for LHC Run 3 and Run 4. The event rates are dominated by charm hadron decays, contributing significantly to the muon and electron neutrino rates and all of the tau neutrino rate. The central predictions for neutrino event rates are derived from event generators, with uncertainties based on scale variations. The predicted event rates for Run 3 are approximately 1700, 8500, and 30 for electron, muon, and tau neutrinos, respectively, and for Run 4, 4900, 25000, and 90. These rates imply percent-level statistical uncertainties for electron and muon neutrino studies, while tau neutrino studies will benefit from a large increase in observed events. The energy and spatial distributions of neutrinos are analyzed, showing that muon neutrinos are more collimated than electron and tau neutrinos. The spatial distribution in the transverse plane is shown for different neutrino species, with muon neutrinos being more collimated than electron and tau neutrinos. The distribution of interacting neutrinos in the (x, Energy) plane is also shown, with the highest-energy neutrinos focused along the LOS. The energy spectra of neutrinos are presented, with the central prediction based on event generators and uncertainties from flux and cross-section variations. The results indicate that FASER will be sensitive to both leading and sub-leading contributions to neutrino eventThe FASER Collaboration has updated simulations and presented theoretical predictions for neutrino fluxes and cross sections, along with their uncertainties, to support future neutrino measurements at the LHC. FASER, located 480 m from the ATLAS interaction point, has detected collider neutrinos for the first time, with 153 muon neutrinos observed in 2022. The experiment is expected to collect 250 fb⁻¹ in LHC Run 3 and 930 fb⁻¹ in Run 3 + Run 4. These neutrino event rates, along with their energy and spatial distributions, will enable studies of neutrino scattering cross sections, forward hadron fluxes, parton distribution functions, and new physics. Neutrino fluxes are primarily produced by the weak decay of light and charm hadrons. The fast neutrino flux simulation, based on Monte Carlo event generators, has been updated for LHC Run 3 and Run 4 configurations. The simulation accounts for beam crossing angles, magnetic fields, and hadron production. The neutrino flux is estimated using the fast neutrino flux simulation, validated against full simulations. The flux uncertainties are mainly due to hadron production modeling, while interaction cross sections are modeled using the Bodek-Yang model and newer NLO structure function models. These models are compared, and cross-section uncertainties are defined. The neutrino event rates for electron, muon, and tau neutrinos are predicted for LHC Run 3 and Run 4. The event rates are dominated by charm hadron decays, contributing significantly to the muon and electron neutrino rates and all of the tau neutrino rate. The central predictions for neutrino event rates are derived from event generators, with uncertainties based on scale variations. The predicted event rates for Run 3 are approximately 1700, 8500, and 30 for electron, muon, and tau neutrinos, respectively, and for Run 4, 4900, 25000, and 90. These rates imply percent-level statistical uncertainties for electron and muon neutrino studies, while tau neutrino studies will benefit from a large increase in observed events. The energy and spatial distributions of neutrinos are analyzed, showing that muon neutrinos are more collimated than electron and tau neutrinos. The spatial distribution in the transverse plane is shown for different neutrino species, with muon neutrinos being more collimated than electron and tau neutrinos. The distribution of interacting neutrinos in the (x, Energy) plane is also shown, with the highest-energy neutrinos focused along the LOS. The energy spectra of neutrinos are presented, with the central prediction based on event generators and uncertainties from flux and cross-section variations. The results indicate that FASER will be sensitive to both leading and sub-leading contributions to neutrino event