How do I delete phones from one device and have them delete from all devices? When I take a picture it shows up in the iCloud photos of each device and "says" it will be removed from every device when I hit delete, but it doesn't actually happen...!

Are you using Photostream or the iCloud Photo Library? If it's the iCloud photos library, they should delete everywhere, though they retain them temprarily in a "recently deleted" album.

If you're using Photostream, they don't necessarily delete everywhere. This link explains it pretty well: Delete photos from My Photo Stream - Apple Support

Well, you're right! That's peculiar. How many devices and what type are you syncing? Have you pinpointed which device is keeping deleted pictures? And I'll ask if you've gone into the settings to double check each device, but I know that's obvious. The only setting I can think of that may cause a delay is that your mobile devices may not be setup to sync with cellular. Also, if your initial iCloud library setup and sync has not completed, you may not get updates until that is done.