We present HIRES/Keck spectra having resolution similar to 6 km s(-1) of Mg II lambda 2796 absorption profiles that arise in the gas believed to be associated with 15 identified galaxies over the redshift range (0.5 less than or equal to z less than or equal to 0.9). These galaxies have measured redshifts consistent with those seen in absorption. Using nonparametric rank correlation tests, we searched for correlations of the absorption strengths, saturation, and line-of-sight kinematics with the galaxy redshifts, rest frame B and K luminosities, rest (B-K) colors, and impact parameters D. We found no correlations at the 2.5 sigma level between the measured absorption properties and galaxy properties. Of primary significance is the fact that the QSO-galaxy impact parameter apparently does not provide the primary distinguishing factor by which absorption properties can be characterized. The absorption properties of Mg II selected galaxies exhibit a large scatter, which, we argue, is suggestive of a picture in which the gas in galaxies arises from a variety of ongoing dynamical events. Inferences from our study include the following: (1) The spatial distribution of absorbing gas in and around galaxies does not appear to follow a simple galactocentric functional dependence, since the gas distribution is probably highly structured. (2) A single systematic kinematic model apparently cannot describe the observed velocity spreads in the absorbing gas. It is more likely that galaxy/halo events giving rise to absorbing gas each exhibit their own systematic kinematics, so that a heterogeneous population of subgalaxy scale structures are giving rise to the observed cloud velocities. (3) The absorbing gas spatial distribution and overall kinematics may depend upon gas-producing events and mechanisms that are recent to the epoch at which the absorption is observed. In any given galaxy, these distributions likely change over a similar to few Gyr timescale (few dynamical times of the absorbing clouds), which provides one source for the observed scatter in the absorption properties. Based upon these inferences, we note that any evolution in the absorption gas properties over the wider redshift range (0.4 less than or equal to z less than or equal to 2.2) should be directly quantifiable from a larger data set of high-resolution absorption profiles.