1) Even though the AMM engine checks neglect the effect of humidity / liquid water content. the test cell corrections include humidity effects (most of the liquid rain gets removed by the large low-velocity inlet area of the test cell).
2) I'd expect the N1/N2/(N3) relationship to change as the rain changes state to water vapor in the compression process.
But whether N1 changes will depend on the design of the control system. Since modern engines often control N1 directly, the rain should result in N1 remaining steady, and N2 varying. Older engines (early CF6's e.g.) have no N1 control, only N2, so N1 can indeed "float".