Galaxies are the fundamental building blocks of the Universe. They are made of stars, interstellar gas, dust, and dark matter. During their life, galaxies convert the available gas into new stars and dust plays a key role in aiding star formation. This program will revolutionize our understanding of galaxy evolution at different cosmic epochs, exploiting space-based observations that for the first time will give us access to some critical near infrared lines for large samples of galaxies. Exploiting data from two among the first programs ever approved for the James Webb Space Telescope (JWST), we will measure both integrated and spatially resolved extinction-corrected star formation rates, gas ionization properties, and metallicities across the "Cosmic Noon" (z=1-3.5) and in galaxies in different environments at the "Cosmic Dusk" (z 1), reaching down to stellar masses of 1e7 Msun -- a completely uncharted territory --, enabling key tests of theoretical models at 0.5 kpc resolution. We will analyze Paschen and Balmer emission line fluxes in star forming galaxies, comparing results based on the two different star formation rate tracers characterized by a different dust obscuration. We will hence quantify the amount of star formation enshrouded by dust and not visible at optical wavelengths. We will compute gas metallicities from optical lines and constrain the evolution of the mass-metallicity relation to determine the role of gas recycling at different epochs, and quantify the role of feedback and of the stochastic processes in regulating metallicity. Radial gradients will provide the crucial data to test "inside-out" scenarios of star formation, whereby galaxies form the bulge first, and then grow their disk structure. Gas metallicity gradients will allow us to understand short-duty-cycle events of very strong feedback. We will therefore obtain an unprecedented view on the processes regulating galaxy evolution over more than half of the life of the universe. The proposed analysis is extremely timely as JWST is about to start observations and will have a huge impact on the worldwide scientific community, showing the first results obtained with JWST observations and helping future observations.