You will actually be fine with mismatched tires on the rear. I have run nearly every size and type of tires on my 370Z (including mismatched tires, different rim diameters, and grossly mis-sized tires) and have never had a problem with the ABS or traction control (if you run a really squishy all season or a Toyo T1-R you will have ABS kicking in a lot however).
That being said it is not ideal for any serious autocross or track days. But it sounds like you are not really that serious into autocross that it would matter.
And yes there are faster tires than the RE-11 in the hands of an experienced driver.
305's fit fine on the Sport Stock rear wheel. However, if you do it you should only do it for looks (which is fine) because that size tire is too pinched to get all the tread on the road surface and it is heavier.
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