The Xe-129 NMR shielding and diffusion of xenon dissolved in the chiral liquid-crystal 1-methylheptyl 4'-(4-n-decyloxybenzoyloxy)biphenyl-4-carboxylate (10B1M7) were studied over the temperature range covering the isotropic (1), smectic A (SmA), and ferroelectric, ferrielectric, and antiferroelectric smectic C*(SmC*) phases. The Xe-129 shielding reveals clearly the I-SmA and SmA- SmC*(ferroelectric) phase transitions. The SmC* sub-phase transitions can also be detected by smaller but distinguishable shifts of the shielding accompanied by line width changes. A theoretical model developed earlier is applied to the shielding data, confirming a negative anisotropic contribution to the shielding as the SmA phase forms and allowing the evaluation of the tilt angle in the SmC*. Diffusion experiments were mostly performed in the direction parallel to the layer normal, i.e., along the external magnetic field, D-11, in the smectic phases but a few experiments were carried out in the in-plane direction, i.e., perpendicular to the external magnetic field, Dproves , as well. These experiments indicate large anisotropy, Dproves /D-11, of the Xe-129 diffusion tensor that increases as the temperature decreases. Application of the Arrhenius equation to the temperature-dependence of D-11 reveals different activation energies for each studied phase. This can be correlated to changes in the smectic layer structure that occur between the different smectic phases.