Interpretation of radiation resistance in receiving mode
No, in general, there is no such effect as reradiation. This heavily depends on the antenna type. The radiation resistance is a model for the radiation. Due to reciprocity, one should still match to this resistance in the receive case, but the simple model as you describe it (a voltage source in series with the antenna feedpoint impedance) is not valid in the receive case. 

Generally, all power accepted by the antenna (described, e.g., by the effective aperture size) is received. Any other amount can be scattered by the antenna, but this is related to geometrical features of the antenna and, in the matched case, by no means always 50% of the power, but a rather arbitrary value.