The uniform magnetic susceptibility of La_2-xSr_xCu_1-yZn_yO₄ has been investigated over a wide range of impurity (Zn) concentration for different planar carrier (hole) content, p (º x, for this system), extending from underdoped to heavily overdoped regions. A doping dependent Zn-induced magnetic behaviour is observed for these compounds. The apparent Zn induced moment (expressed as p_eff²/Zn in units of m_B²) is larger in the underdoped side and, decreases quite sharply around p ~ 0.19,without much change for further overdoping. This indicates a possible role of the pseudogap on the Zn induced magnetic behaviour, as there are indications that the pseudogap is present only for p £ 0.19. It is shown that the data can also be interpreted in terms of a Zn-induced low energy quasiparticle resonance that depends on the presence of the pseudogap. The oxygen isotope exponents in superconducting transition temperature and superfluid density, a(T_c) and ap_s), respectively, have been studied as a function of hole (x) and impurity (y) contents in La_2-xSr_xCu_1-yZn_yO₄. The isotope exponents displayed a canonical relationship, except around the region of x ~ 1/8. The results are discussed in terms of the presence of the pseudogap and the stripe correlations. In-plane resistivity measurements under applied magnetic fields (up to 12 Tesla), p_ab(T,H), have been carried out on c-axis oriented thin films of Y_0.95Ca_0.05Ba₂(Cu_1-yZn_y)₃O_7-d with varying amount of in-plane disorder (Zn) and hole concentration. Following an earlier work on sintered compounds of the same system, we have obtained supplementary information about the characteristic pseudogap temperature, T*(p), from the analysis of the p_ab(T,H) data. Our thin film data support the earlier findings that T*(p) falls below T_c0(p) (º T_c(p) for pure compound) in the overdoped side and, extrapolates to zero at p ~ 0.19.