Usually it only takes a couple days. For better details look in at www.iowacarry.org There are a lot of Polk county members that could answer your questions in detail.
As for open carry, yes but no. You can carry in unincorporated areas of the state while not in a vehicle. So.... Not in a state park, not on someone else's land (unless you have permission to be there), not in a vehicle. One would have to ask where this does apply? The only place I open carry is on public hunting ground. It's unincorporated, and frequently a beautiful place to take a walk.