In this dissertation I undertook two projects, which together aim to push the bounds of our understanding of galaxy evolution and cosmology and prepare for upcoming facilities. For the former, I studied the population of strongly lensed, dusty star-forming galaxies who contribute to the majority of star formations at the most intensely star-forming period of the universe. I performed lens modeling and source reconstruction on five of these galaxies and studied the intrinsic size, differential magnification and molecular gas properties of them. I found that the reconstructed region of CO emission is less concentrated than the region emitting dust continuum, and that ignoring the differential magnification effect can bias the estimate of physical properties of interstellar medium of the galaxies. I modified previous visibility-based lens model to work on optical especially the James Webb Space Telescope data, and made the model capable of estimating lens parameters with joint optical and radio data. I tested the new model on simulated observations as well as the Hubble Space Telescope data and the Atacama Large Millimeter/submillimeter Array data of the galaxy SDP.9. The estimated parameters for SDP.9 are consistent with previous analyses based on optical or radio data alone. The techniques developed as part of this work are designed to be applicable to our team's James Webb Space Telescope Early Release Science observations.For the latter, I developed end-to-end cosmological redshift drift simulations. We can in principle measure the history of cosmological expansion through a redshift drift experiment using the Lyman-alpha forest spectra of high-redshift bright quasars. I simulated mock redshift drift observations with spectra from the Sloan Digital Sky Survey and the Keck telescope's High Resolution Echelle Spectrometer to quantify the instrumental requirements for the proposed experiment. In considering the sensitivity of a dedicated facility, I found that redshift drift can be detected via Lyman-alpha forest observation at S/N = 3 (5) in 15 (22) years with a 25 m telescope, given a spectrograph with long term stability with R = 50,000 and an efficiency of 25%.