We perform consistent reductions and measurements for three ultra-faint dwarf galaxies (UFDs): Bootes I, Leo IV, and Leo V. Using the public archival data from the GIRAFFE spectrograph on the Very Large Telescope (VLT), we locate new members and provide refined measurements of physical parameters for these dwarf galaxies. We identify nine new Leo IV members and four new Leo V members, and perform a comparative analysis of previously discovered members. Additionally, we identify one new binary star in both Leo IV and Leo V. After removing binary stars, we recalculate the velocity dispersions of Bootes I and Leo IV to be 5.1_-0.8_^+0.7^ and 3.4_-0.9_^+1.3^km/s, respectively; we do not resolve the Leo V velocity dispersion. We identify a weak velocity gradient in Leo V that is ~4x smaller than the previously calculated gradient and that has a corresponding position angle that differs from the value in the literature by ~120{deg}. Combining the VLT data with previous values from the literature, we reanalyze the Bootes I metallicity distribution function and find that a model including infall of pristine gas, while Bootes I was forming stars' best fits the data. Our analysis of Leo IV, Leo V, and other UFDs will enhance our understanding of these enigmatic stellar populations and contribute to future dark matter studies. This is the first in a series of papers examining 13 UDFs observed with VLT/GIRAFFE between 2009 and 2017. Similar analyses of the remaining 10 UFDs will be presented in forthcoming papers.