Answer: Since numerous flowers are borne on a single stem you have a choice. Either pick off individual spent flowers, or wait until they are all spent and clip off the entire stem. I'm a hopeful gardener so I simply pick off the individual flowers just as the petals begin looking worn but before they fall off. If you don't pinch the faded flower off then, a seed pod will form which looks very similar to an unopened flower bud. The purpose of deadheading is to remove spent flowers before the plant spends energy developing seeds (the hard green pod you describe). Therein my hope lies: the plant will redirect its energy into producing more flowers rather than developing seeds.
Irises are typically dug and divided in late summer (July or August). The foliage will remain green until frost so don't use that as an indication that it's safe to move them. Simply wait until after they've finished blooming to dig and divide them. Now would be a good time.
Best wishes with your garden!
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