The permit to purchase does not have any classroom time so you can purchase a handgun with no knowledge of how to use it. It is good for one year and is the background check done by the sheriff's office rather than your FFL. You still fill out the paperwork at your FFL, but they do not always do a background check if you have the permit to purchase.
You are correct that the permit to carry also counts as a permit to purchase (good for 5 years). Again, the background check is already done if you have that permit.
And you are correct that there is no waiting period to purchase.
I am pretty sure private sellers in IA do not have to do much for a background check. It wound be wise to do a bill of sale that includes the guns serial number, and make sure you don't sell to a minor.