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Since the calculation of IP3 involves the difference between the fundamental and the average of the key troublemaking anti-social neighbours; (2f1-f2)-LO, (2f2-f1)-LO (or upconversion LO-(2f1-f2), LO-(2f2-F1) ), the contribution of IM products of the first-stage mixer of the spectrum analyzer is subtracted out.
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I'm not sure what you mean here, but in the simplistic case of the DUT being an RF amplifier, then the analyser IMD levels need to be about 20dB lower than the IMD levels of the amplifier if the aim is to keep the measurement uncertainty of the amplifier IMD below about +/-1dB. Otherwise, the analyser IMD tones can sum or cancel with the IMD tones of the DUT and cause uncertainty exceeding +/- 1dB.
If the input TOI of the analyser is the same as the output TOI of the DUT, then the DUT IMD and analyser IMD tones will be at the same level, and they generally sum together in the analyser and the analyser will then display the IMD levels about 6dB higher than the true IMD level of the DUT. The tones can also cancel (in theory) and the analyser might show much lower distortion than the true result. That's why the analyser IMD levels ideally need to be about 20dB lower than the IMD levels of the DUT.