We present custom-processed ultraviolet, optical, and near-infrared photometry for the REsolved Spectroscopy of a Local VolumE (RESOLVE) survey, a volume-limited census of stellar, gas, and dynamical mass within two subvolumes of the nearby universe (RESOLVE-A and RESOLVE-B). RESOLVE is complete down to baryonic mass ~10^9.1-9.3^M_{sun}_, probing the upper end of the dwarf galaxy regime. In contrast to standard pipeline photometry (e.g., SDSS), our photometry uses optimal background subtraction, avoids suppressing color gradients, and employs multiple flux extrapolation routines to estimate systematic errors. With these improvements, we measure brighter magnitudes, larger radii, bluer colors, and a real increase in scatter around the red sequence. Combining stellar mass estimates based on our optimized photometry with the nearly complete HI mass census for RESOLVE-A, we create new z=0 volume-limited calibrations of the photometric gas fractions (PGF) technique, which predicts gas-to-stellar mass ratios (G/S) from galaxy colors and optional additional parameters. We analyze G/S-color residuals versus potential third parameters, finding that axial ratio is the best independent and physically meaningful third parameter. We define a "modified color" from planar fits to G/S as a function of both color and axial ratio. In the complete galaxy population, upper limits on G/S bias linear and planar fits. We therefore model the entire PGF probability density field, enabling iterative statistical modeling of upper limits and prediction of full G/S probability distributions for individual galaxies. These distributions have two-component structure in the red color regime. Finally, we use the RESOLVE-B 21cm census to test several PGF calibrations, finding that most systematically under- or overestimate gas masses, but the full probability density method performs well.