The physical conditions of molecular gas in galaxies, and the impact of star formation and AGN on these conditions and on the emergent stellar IMF, are overarching themes in astrophysics. We are entering an era where numerical simulations of turbulent molecular gas can be informed and constrained by observations of such gas. I propose to investigate, theoretically and observationally, the impact of merger-driven star formation during a vital period in cosmic history, 1 < z < 3, when much of today’s stellar mass was formed. It is here that we must study Larson’s star-formation laws, and turbulence-regulated aspects of star formation, and look for possibly dramatic differences in the initial conditions of star formation, and the different IMF these may impose. These galaxies were significantly more gas-rich and turbulent than local starbursts, with different fragmentation histories and higher star-formation-rate densities (so more cosmic rays). They should yield cleaner signatures of a top-heavy IMF than local starbursts, where periods of ordinary star formation may have diluted such signatures. I will exploit strongly lensed starbursts to study powerful diagnostic rest-frame FIR cooling lines with Herschel's FTS and map velocity fields with JVLA/ALMA, moving beyond studies of integrated galaxy properties to study the activity within starbursts on sub-kpc scales, distinguishing between fueling mechanisms and testing Larson's relations. At this level of sophistication, the analysis of the ISM at z > 1 begins to be comparable to that possible at z ~ 0. Abundances - probed by multi-species, multi-J isotopologues and molecular diagnostics - will reveal the dominant form of nucleosynthesis enriching their ISM, and gravo-turbulent MHD simulations of gas fragmentation in cosmic-ray-dominated regions will determine how turbulent energy injection affects merger-driven systems, producing IMF libraries as functions of ISM conditions to determine the cosmological consequences.