Do I need to dig the whole clump up when dividing or can I just dig half the clump?
You can dig up as much of it as you want, but if, as may be the case, the whole clump is thick and in need of dividing, then dig up the whole thing. You'll be doing yourself and the plants a favor (new lease on life). Just my $.02.
Frequently I dig away half the clump. Since this leaves fresh cut rhizomes I make sure those cuts are open to the sun (move dirt if necessary). Don't allow water come in contact for a few days.
I will sometimes just take the shovel and cut off half the clump and then take that half I removed and break that up and replant.
It might not be the perfect gardener thing to do, but it works fine and it is faster.
It makes a difference how valuable the variety of iris is.
Possibly silly questions - what tool do you use to dig them up? Shovel? Potato fork? I know you start out far enough that you don't slice a rhizome, and you want to damage roots as little as possible...
I use a spade.