I added a Microsoft Exchange account to my iOS Mail app and I am retrospectively scared of the administration warning.

They can not view any data on your phone. They can see what’s in your Exchange account, but they can do that no matter what.

They can enforce policies on your phone such as passcode requirements, encrypted backups, restrictions on the camera, etc.

They can also erase your entire device if they choose to do so.

If that makes you unhappy, remove the account from your device.

The Exchange server can control many aspects of the iPhone including wiping the device. They can also impose other security measures through the Exchange profile such as passcode requirements and certain restrictions.

They can't view your data or files though.

Yes, so long as you did not install a management profile as part of setting up the account on your device. If you did, you will also need to delete the management profile.