Accelerator neutrino oscillation experiments provide a sensitive way to investigate a number of major open questions in neutrino physics. To achieve precision neutrino oscillation measurements, we need a good understanding of key aspects of the experiments, such as the detection technologies used and neutrino interactions at few-GeV energies. The MicroBooNE experiment has advanced the development of technologies for LArTPCs. An ultra-violet laser system was introduced to MicroBooNE in order to measure the electric field in situ, which plays a central role in the formation of charge and light signals in LArTPCs. This thesis describes the setup and operation of the laser system. I developed a general methodology to measure the electric field and the consequent spatial distortion in LArTPCs, which supports precision measurements in accelerator neutrino oscillation experiments. In MicroBooNE, the measured electric field distortions are up to 15 ± 3% with respect to the nominal value, and the measured spatial distortions are up to 15 ± 3 cm. The result of the electric field measurement is applied to the detector simulation and the event reconstruction, which leads to a better detector characterization for neutrino analyses. A significant concern for measurements of neutrino interactions is model dependence, as the currently available models are not sufficient for describing the picture of neutrino interacting at few-GeV energies. In this thesis, I developed a detailed strategy for a model-independent cross-section measurement at low energy transfers, where the available model predictions do not agree with the inclusive measurements from multiple experiments. A likelihood fit technique for cross-section extraction is realized in an accelerator neutrino experiment using a LArTPC for the first time. The treatment of systematic uncertainties developed in this thesis is generally applicable for analyses using similar fitting techniques. This neutrino interaction study at low energy transfers provides a probe to the poorly understood region of neutrino cross sections. The measurement scheme developed here aims to guide future model-independent cross-section measurements, particularly for neutrino experiments using LArTPCs.