Understanding the interplay between screening, electronic correlations, and collective excitations is essential for the design of two-dimensional quantum materials. Here, we present a comprehensive first-principles study of more than 60 MA2Z4 monolayers, encompassing semiconducting, metallic, cold-metallic, magnetic, and topological phases. Using the constrained random phase approximation (cRPA), we compute material-specific effective Coulomb interaction parameters U, \(U^{\prime}\) , and J, including their spatial dependence across distinct correlated subspaces defined by local coordination and crystal symmetry. In semiconducting compounds, long-range nonlocal interactions persist, revealing unconventional screening and suggesting strong excitonic effects beyond simple dielectric models. In cold-metallic systems, sizable long-range Coulomb interactions remain despite the presence of free carriers, highlighting their atypical metallic screening. Among 33-valence-electron compounds, we find \(U^{\mathrm{eff}}\,{>}\,W\) in the β2 phase, indicating proximity to charge-density-wave or Mott instabilities. Several V- and Nb-based systems exhibit intermediate-to-strong correlation strength, with U/W > 1 in multiple cases. Using cRPA-derived Stoner parameters, we identify magnetic instabilities in various V-, Nb-, Cr-, and Mn-based compounds. Finally, selected cold-metallic systems display plasmon dispersions that deviate from the conventional \(\sqrt{q}\) behavior, revealing nearly non-dispersive low-energy modes. These results position MA2Z4 monolayers as a versatile platform for investigating correlation-driven instabilities and emergent collective behavior in two dimensions.
