A series of polycrystalline samples and submillimeter size single crystals of a cuprate oxychloride Ca2-xNaxCuO2Cl2 (Na-CCOC) with values of Na content ranging from underdoped to optimally doped regions were synthesized at pressure of 30-55 kbar and temperature of 1250-1700 °C. A systematic variation of the transition temperature Tc with a maximum value of 29 K for xapprox0.20 has been found as a function of Na content. In order to check the role of the apical oxygen for high-temperature superconductivity, we performed muon-spin rotation and magnetization studies of the in-plane magnetic penetration depth λabfor Ca2-xNaxCuO2Cl2 samples with xapprox0.11, 0.12, 0.15, 0.18, and 0.19. The absolute value of the in-plane magnetic penetration depth at T=0 was found to increase with decreasing doping from λab(0)=316(19) nm for the xapprox0.19 sample to λab(0)=430(26) nm for the xapprox0.11 one. Based on a comparison of the present Na-CCOC data with the data of La2-xSrxCuO4 cuprate superconductors, it is concluded that replacing of apical oxygen by chlorine decreases the coupling between the superconducting CuO2 planes, leading to an enhancement of the two-dimensional properties of Na-CCOC. The torque studies implies that the anisotropy coefficient λ=84(1) of Ca1.82Na0.18CuO2Cl2 single crystals is much more enhanced compared to the structurally related La1.82Sr0.18CuO4 where for same doping λ is much lower, i.e. γ approx 11.