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Any party to the proceeding has the right to cross examine on any affidavit relating to the proceeding so R can cross-examine A if A has filed an Affidavit for the motion.
If A has not file any affidavit then there is nothing to be cross-examined on and R can only defend the application for Summary Judgment by putting all evidence in R's Affidavit.
R does not have to serve A with P's motion material. R doesn't have to serve P with the response either unless A has become involved in the motion and filed materials.
I am going to opt out and let another expert step in who may know more about this issue.