Thank you. Both good suggestions.
Unfortunately Apple Support couldn’t help. Senior specialist said that I can’t expect an iPad backup to restore correctly to an iPhone because the iOS is written differently. Told me that the display scales are different so photos and videos taken on an an iPad and backed up won’t restore to an iPhone. I asked why all of the apps transferred along with notes, contacts, calendar, etc. and was told that I was lucky that this worked. That was the explanation for why restoring a backup from iCloud didn’t work for Photos and iMessages.
As far as why iMessages and Photos won’t just sync from iCloud onto the new device anyway (since we use iMessages and Photos in the cloud) there is no explanation for iMessages and I may hear back from the engineers sometime after the new year. iMessages were all in the cloud but wouldn’t sync to the new device, however, iMessages created on the new device do sync to the old device.
One thing I learned is that Photos in iCloud does seem to be working correctly. This issue is that not all of the photos from the iPad have been pushed to iCloud. All of the photos that were uploaded from the old device to iCloud Photos are synced on the new device. Not clear why all photos weren’t pushed to the cloud from the old device. This also doesn’t explain why all 4.6 GB of iMessages in the cloud wouldn’t sync to the new device though. They were all in iCloud and just wouldn’t sync.
An iTunes backup is another good point. In my situation I have an obstacle. I bought a MacBook Pro with the touchbar. I don’t use it much anymore because it is buggy and the touch bar went haywire and flashes constantly and it is very irritating. My hard drive is 500 GB, so backing up just my and some family members iOS devices alone used nearly all of the hard drive. I had to move our photo library to an external drive. There isn’t enough room to backup this family member’s device to my MacBook Pro so I would need more storage.
I looked into doing a backup of the device to an external hard drive but once it got into command prompts and changing paths and other technical things I dropped it. If there is a simpler way to backup to an external drive I suppose I could look into that again. The reason I pay the $10 a month for iCloud for our family to backup to is because I looked at it as the rough equivalent to backing up our iOS devices to an external drive. I can look more into this.
If if I get any info that is helpful I will post. Otherwise may just have to erase the phone and setup as new and see if things work a second time. Otherwise thanks for the suggestions. I’m exhausted.
This is the error message that I previously posted.