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I need help with determining if the lower scores are indicative of a serious weakness or if they are relative weaknesses.

Really, the only one who can determine that for sure would be a professional who actually observes your DS. I, as a total amateur, can tell you that a low processing speed does not necessarily indicate a serious weakness; my son's is in the 21st percentile and he does well in school.

Your previous tester should have calculated the GAI since there is such a disparity in the test results that indicate an invalid FSIQ. Did s/he do that?