w_sohl,
Yes, with two outs, the batter is out.
With less than two outs, the batter is still out.
The only time R3 is out is when the batter interferes with the catcher's attempt to retire an R3 who is attempting to advance on the pitch (i.e. squeeze or steal).
If the batter happened to strike out on the pitch, the runner who was being played upon is out.
JM
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