Spatially resolved spectroscopy has been obtained for a sample of 27 star-forming (SF) galaxies selected from our deep Hα survey of the Hercules cluster. We have applied spectral synthesis models to all emission-line spectra of this sample using the population synthesis code STARLIGHT and have obtained fundamental parameters of stellar components such as mean metallicity and age. The emission-line spectra were corrected for underlying stellar absorption using these spectral synthesis models. Line fluxes were measured and O/H and N/O gas chemical abundances were obtained using the latest empirical calibrations. We have derived the masses and total luminosities of the galaxies using available Sloan Digital Sky Survey broadband photometry. The effects of cluster environment on the chemical evolution of galaxies and on their mass-metallicity (MZ) and luminosity-metallicity (LZ) relations were studied by combining the derived gas metallicities, the mean stellar metallicities and ages, the masses and luminosities of the galaxies, and their existing H I data. Our Hercules SF galaxies are divided into three main subgroups: (1) chemically evolved spirals with truncated ionized-gas disks and nearly flat oxygen gradients, demonstrating the effect of ram-pressure stripping; (2) chemically evolved dwarfs/irregulars populating the highest local densities, possible products of tidal interactions in preprocessing events; and (3) less metallic dwarf galaxies that appear to be "newcomers" to the cluster and are experiencing pressure-triggered star formation. Most Hercules SF galaxies follow well-defined MZ and LZ sequences (for both O/H and N/O), though the dwarf/irregular galaxies located at the densest regions appear to be outliers to these global relations, suggesting a physical reason for the dispersion in these fundamental relations. The Hercules cluster appears to be currently assembling via the merger of smaller substructures, providing an ideal laboratory where the local environment has been found to be a key parameter in understanding the chemical history of galaxies.