Assume we have an antenna in receiving mode, connected to a matched load. The equivalent circuit is a voltage source in series with the antenna feedpoint impedance and the load impedance. As we know, the feedpoint impedance is made up of a reactive component, an ohmic resistance and a radiation resistance. Now, since the load is matched, half of the intercepted power will be delivered to the load, while the other half will be delivered to the ohmic and radiation resistances respectively. The power delivered to the ohmic resistance will be converted into heat, but how to interpret the power delivered to the radiation resistance? Is this part of the total power reflected by the antenna?
Yes, it is effectively radiated back by the antenna. If the antenna is receiving from a point source, but its radiation pattern is not pointing only at the source (e.g. is isotropic), this radiation will go in 'all' directions. Thus the antenna will redirect (reflect) the incoming signal back in a broader beam.
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.