You should cut back the foliage. I have read/heard that about 5 inches is good. This will allow the rhizomes to grow new roots. New foliage will start to grow later in the summer. The rhizomes are strong and they will survive - even thrive if you thinned them out some.

Yes go ahead and trim the fans back now. Since you are in the middle of a heat wave, keep the irises watered...but dont overwater...once you see new growth on the fans you know your irises are happy and you should be able to discontinue extra watering.. My heat index was almost 110 here so I understand heat wave.

I don't see how you can avoid trimming when moving/dividing them. Iris are supposed to be planted essentially on top of the soil, with the top surface fairly exposed - that's what they like. If you fail to trim, the flags will just tip the rhizomes out of the soil altogether. The roots grow to hold things in place, and the flags grow back as the plant can support them.