Starting from the symmetrical ps meson theory, the relativistic and exchange current corrections to the thermal N-P capture cross section and the deuteron magnetic moment have been defined unambiguously and calculated using the T-D formalism up to the lowest order of the meson-nucleon coupling constant and the nucleon velocity. This work is a refinement and generalization of the previous paper on the exchange current correction to the deuteron moment, the result of which is also obtained here. With respect to the relativistic corrections, quite a different method is used. Numerical values of these corrections are then estimated by using the phenomenologically adjusted two nucleon wave functions with or without the hard core. The sum of these correction is shown to be about +1% of the capture cross section and about -2% of the magnetic moment. The phenomenological thermal N-P capture cross section is also estimated and is shown to agree with the experimental one within much larger experimental and theoretical ambiguities than the above correction. As the exchange current correction is reduced very much if the D-state probability is chosen to be smaller and there may be in addition some small positive non-additivity correction, the deuteron D-state probability is finally estimated as 3±1% or so, the same value as was reported previously.