iCloud stored messages I can't see on iCloud.com & photos sneaking into iCloud from my iPhone?

iCloud Backup never deletes anything from your device(s).

If you delete an iCloud Backup and then do another iCloud Backup later, nothing will be deleted from your phone.

Also note that you said

"I delete the previously backed up iCloud.com photos to open storage on iCloud. If a few months later, I set my iPhone photos iCloud Backup to "on", ..."

You cannot delete "previously backed up iCloud.com photos" -- you can only delete an entire iCloud Backup as described in Manage your iCloud storage - Apple Support

The photos that you can see at iCloud.com are not iCloud Backup -- they are iCloud Photos and are not there because of iCloud Backup.

The information in Use Messages in iCloud - Apple Support has instructions on how to turn off iCloud Messages if you want to do that. It also includes the following explanation about why you can't view the messages on iCloud.com:

You can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch, and Mac. For your privacy, Messages in iCloud is end-to-end encrypted,* which means you can't view or access Messages online via browser. 

The photos that you can see on iCloud.com are not there because of iCloud Backup; they are there because iCloud Photos is (or was) turned on. If you delete the photos from iCloud.com they will also be deleted from any device where iCloud Photos is on. See more information in Set up and use iCloud Photos - Apple Support

Deleting iCloud photos is the same no matter how you have "the backup option" set (I'm assuming you mean iCloud Backup). iCloud Backup and iCloud Photos are two completely different things and the only relationship between the two is that the photos won't be included in iCloud Backup if you have iCloud Photos turned on.

If you delete photos from iCloud Photos, they are gone (after approximately 30 days in Recently Deleted) from iCloud and any device where iCloud Photos is tuned on -- there is no option to do anything with them after that.

If you turn off iCloud Photos as described in Get help with iCloud Photos - Apple Support then the photos will be included in the next iCloud Backup (assuming you haven't deleted them).