Mercury-based cuprates HgBa2CuO 4+δ with 0 < δ < 0.2 (Hg1201) are the superconductors with a single CuO2 layer in unit cell and the optimally oxidized one has the highest Tc = 98 K among the ever reported single-CuO2-layer superconductors. Double CuO2 layered cuprates HgBa2CaCu2O 6+δ with 0.05 < δ < 0.35 (Hg1212) have the highest Tc = 127 K at the optimal oxygen concentration. This is the highest Tc among the ever reported double-CuO2-layer superconductors. The Hg1201 has the nearly perfect fat CuO2 plane. The Hg1212 has the flattest CuO2 plane among the other lower Tc double-layer cuprates, which is associated with the mystery of the highest Tc. Both systems have a pseudo spin-gap in the magnetic excitation spectrum of the normal states. In this article, we present the microscopic studies of magnetic and electric properties of the Hg-based superconducting cuprates using nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) techniques. NMR and NQR are powerful to detect local information through the nuclear sites in materials and have supplied us with information on low frequency magnetic response of electronic systems. Although the structure analysis indicates the flat CuO2 planes, zero field 63,65 Cu NQR spectra, which are sensitive to local electric charge distribution, show inhomogeneous broadening. The local electrostatic states are rather inhomogeneous. Although the d-wave superconductivity must be fragile to imperfection and non-magnetic impurities, the pure Hg-based superconducting cuprates show impure 63,65 Cu NQR spectra but rather robust pseudo spin-gap in the 63 Cu NMR Knight shift and nuclear spin-lattice relaxation rate over the wide doping regions. There had been an issue whether the pseudo spin-gap results from a double-layer coupling or a single layer anomaly. The NMR results for Hg1201 served as the evidence for the existence of the single-layer pseudo spin-gap. The pseudo spin-gap is explained by a precursory phenomena of superconducting pairing fluctuations or spin singlet correlation. The different doping dependence of the pseudo spin-gap of Hg1201 and Hg1212 is associated with the different Fermi surface contour. The similar temperature dependence of the 199 Hg and the 63 Cu nuclear spin-lattice relaxation times indicates uniform interlayer coupling. The double-layer coupling effect is revisited through the comparison of Hg1201 and Hg1212.