Measurements of the electrical resistivities, Hall coefficients, thermoelectric powers, electronic specific heat coefficients have been carried out for samples of LnFe1-yMyAsO1-xFx (Ln=La, Nd; M=Co, Mn; x=0.11) obtained by M atom dopings to the superconducting LnFeAsO1-xFx (Ln1111) system. The NMR longitudinal relaxation rates 1/T1 have also been measured for samples of LaFe1-yCoyAsO1-xFx with various x values. Co atoms doped to the superconducting LnFeAsO1-xFx are nonmagnetic, and the Tc-suppression by the Co atoms has been found to be too weak to understand by the pair breaking effect expected for the S+- superconducting symmetry proposed as the most probable one for the system. It throws a serious doubt whether the symmetry is realized in this system. Instead of the pair breaking, two mechanisms of the Tc-suppression by the doped impurities have been found: One is the electron localization, which appears when the sheet resistance exceeds h/4e2=6.45 kohm, and another is the disappearance or reduction of the hole-Fermi-surfaces around the gamma point in the reciprocal space. The latter mechanism has been observed, when the electron number increases with increasing Co-doping level and the system changes from an anomalous metal to an ordinary one. On the two distinct T dependences of 1/T1 of LaFeAsO1-xFx, 1/T1 T6 reported by our group in the T region from Tc to ~0.4 Tc for samples with the highest Tc values with varying x, and 1/T1 T2.5-3.0 observed by many groups in the almost entire T region studied below Tc, we discuss what the origin of the difference is, and show that, at least, the T2.5-3.0-like dependence of 1/T1 cannot be considered as the experimental evidence for the S+- symmetry of the order parameter.