The SHINING survey (Paper I; Herrera-Camus et al. 2018) offers a great opportunity to study the properties of the ionized and neutral media of galaxies from prototypical starbursts and active galactic nuclei (AGN) to heavily obscured objects. Based on Herschel/PACS observations of the main far-infrared (FIR) fine-structure lines, in this paper we analyze the physical mechanisms behind the observed line deficits in galaxies, the apparent offset of luminous infrared galaxies (LIRGs) from the mass-metallicity relation, and the scaling relations between [CII] 158 $\mu$m line emission and star formation rate (SFR). Based on a toy model and the Cloudy code, we conclude that the increase in the ionization parameter with FIR surface brightness can explain the observed decrease in the line-to-FIR continuum ratio of galaxies. In the case of the [CII] line, the increase in the ionization parameter is accompanied by a reduction in the photoelectric heating efficiency and the inability of the line to track the increase in the FUV radiation field as galaxies become more compact and luminous. In the central $\sim$kiloparsec regions of AGN galaxies we observe a significant increase in the [OI] 63 $\mu$m/[CII] line ratio; the AGN impact on the line-to-FIR ratios fades on global scales. Based on extinction-insensitive metallicity measurements of LIRGs we confirm that they lie below the mass-metallicity relation, but the offset is smaller than those reported in studies that use optical-based metal abundances. Finally, we present scaling relations between [CII] emission and SFR in the context of the main-sequence of star-forming galaxies.