Measurements of the normal state magnetic susceptibility [chi](T) of YBa2Cu3O7, Bi1.8Pb0.2Sr2CaCu2O8+[delta], and Bi2- xPb xSr2Ca2Cu3O10+[delta] (x = 0.2 and 0.25) were carried out. All [chi](T) data show negative curvature below ~ 2T c. The data for YBa2Cu3O7 are in excellent agreement with a new calculation of the superconducting fluctuation and diamagnetism. From the analysis, we infer s-wave pairing and microscopic parameters are obtained. For [chi](T) of YBa2Cu3O7, part of the negative curvature is inferred to arise from the normal state background. We find a strong temperature dependent anisotropy [delta][chi] ≡ [chi] c - [chi] ab and estimate the normal state spin contributions to [chi](T). The heat capacity C(T) of YBa2Cu3O7 is reported for 0.4 K < T < 400 K in zero and 70 kG magnetic fields. In addition to the feature associated with the onset of the superconductivity at T c, two anomalies in C(T) were observed near 74 K and 330 K, with another possible anomaly near 102 K; the temperatures at which they occur correlate with anomalies in [chi](T) and ultrasonic measurements. The occurrence of the anomaly at ~eq330 K is found to be sample-dependent. The influences of a magnetic field and the thermal and/or magnetic field treatment history dependence of a pellet sample on C(T), the entropy and the influence of superconducting fluctuations on C(T) near T c, and the possible source of the observed intrinsic nonzero [gamma](0) at low T are discussed.