Is there a way in a Configuration Profile to add an Apple ID and Password? This is my scenario working with High School students:
I log in to the App store on a device(s), then scope my free apps to the device and install automatically. Once I'm done installing all apps required I have a profile that removes the App store, Itunes and Imessage. My issue is now the students have the devices at home and when I push new apps, the password is required for installation and don't trust the students with the password. All profiles where setup for me and I was given access to manage our devices.
There is no way to push a profile with the AppleID and password. Apple considers AppleIDs to be personal information.
In addition, you should not be using a single AppleID to install apps on a school-owned device. Instead you should be using Volume Purchasing to purchase Apps and bring them in to Jamf. From there you can scope the Apps to the iPads and have them either install automatically or users can installs them from Self Service.
You will need to integrate your Jamf server with Apple School Manger (do you have an Apple School Manager account?)
Take a look at the Jamf training catalog and the Jamf Administrator's guide on how to setup Volume Purchasing and how to assign Apps to iPads.