Microstrip line ferromagnetic resonance (MS-FMR) and Brillouin light scattering (BLS) in the Damon-Eshbach geometry were used to investigate the perpendicular magnetic anisotropy (PMA), the damping and the interfacial Dzyaloshinskii-Moriya (iDMI) interaction in ferromagnetic (FM)/TaO$_x$-based systems as a function of the ferromagnetic (FM = Co or Co$_8$Fe$_{72}$B$_{20}$) and the TaO$_x$ thicknesses (oxidation level). The analysis of the experimental FMR and BLS data has shown that the effective magnetization, the Gilbert damping parameter α and the iDMI are inversely proportional to the CoFeB and the Co films thickness. The BLS investigation of the iDMI variation versus the TaO$_x$ thickness and oxidation level reveals a contribution of FM/TaO$_x$ mediated by the presence of a Rashba field at this interface. Finally, we evidenced a correlation between iDMI and PMA by varying the Cu spacer thickness in the Pt/Cu/Co/TaO$_x$ system and we showed that both PMA and iDMI are localized at the first atomic monolayers of the Pt/Co interface. The observed non-linear dependence of PMA versus iDMI constant is attributed to similar interface orbital hybridizations involved in both quantities.