The normal and superconducting properties in single crystal Bi2Sr2CaCu2O8 (Bi2212) with T(c) = 86K have been investigated by systematic measurements of the Cu-63 Knight shift, 63K(T) and the nuclear-spin-lattice relaxation time, T1. In the normal state, the T-dependences of 63K(T) and (T1T)-1 in Bi2212 share similar magnetic behaviors to the underdoped systems such as oxygen deficient YBa2Cu3O6+x and YBa2Cu4O8, namely, 63K(T) decreases with lowering temperature and 63(T1T)-1 has a peak above T(c). However, from the analyses of the anisotropy of 1/T1 and the hyperfine field, Bi2212 is found to belong to the slightly over-doped region as in Tl2Ba2CuO6+x and TlSr2CaCu2O8-x. In the superconducting state, the finding of T1T = const. law far below T(c) has revealed that the superconductivity is in a gapless regime, accompanied by the finite density of states at the Fermi level.