Adding another identical winding should do nothing to the operation except decrease the effective secondary winding resistance (and maybe change the leakage inductance a bit). That's all. The RC in the first figure is indeed an RC snubber, though it's somewhat uncommon to put it on the output side, though theoretically it should work the same, since the transformer will reflect it to the primary side anyways. In fact in the figure it shows the same network on both primary and secondary.