It depends on where the app is pulling images from. If you have selected "Optimize iPhone storage" then these apps will only have access to the lower-resolution thumbnails, as bmike pointed out (they use Camera Roll).
Unless the app is specifically coded to pull photos from iCloud Photo Libary (which Apple currently supports), they will just have access to the low-resolution photos stored locally on the device.
All the apps you have mentioned access your Camera Roll, therefore the low-resolution images.
It appears you have synced photos into your iPhone via iTunes. You can select folders from your computer and sync them to your iOS devices when connected (or via Wifi if you have that option checked).
iCloud Photo Library is letting you know you'll lose those synced albums on the phone.
To check which photos and / or videos, you can connect your iPhone to your computer , start iTunes up and go to the Photos section on your device menu:
as you can see, you can select different options to sync photos from your computer back to your iPhone
If you do not remember setting this up, or if it appears un checked, as in my screenshots, you are probably not connected to the original iTunes (or iTunes library) that set this up.
Checking which are the images that will be lost directly on your phone is a bit more tricky, as the only obvious sign is that you cannot delete the album nor the images directly from it. So, you could go checking albums until you find one that does not allows you to delete pictures –although this will also be the case with iCloud Shared albums you joined. The good news is that you probably have a copy of those pictures elsewhere, unless you've lost the computer which synced them in the first place.
Turning My Photo Stream off will stop it from receiving pictures made with other iOS devices or saved on iPhoto / Photos app configured with the service. It will not save space if you don't have other devices behaving in that fashion. It will also stop it to upload them to those other devices, if this is part of your archiving system, keep that in mind.
Turning iCloud Photo Library on will upload a copy of all the pictures taken or saved (but not synced via iTunes) on your iPhone to iCloud, and, depending on the configuration, it will try to save space on your device by erasing the original on your iPhone afterwards and leaving a copy with lower resolution. If this setting is not activated, no space will be saved. Erasing the pictures on your iOS device with iCloud Photo Library on will permanently erase the pictures on all synced devices and on iCloud, so be sure to have a backup.
Best Answer
I’m not sure I can address everything in your post, but here are some things that might help narrow down some options.
Depending on where you split from this general idea - you may or may not have some issues that I didn’t anticipate, but I would probably reach out to Apple Support to verify your iCloud is correct and full and see options to get everything from the phone to iCloud, everything from the Mac to iCloud and then sort out the options.
Getting the local cached copy from the iPhone is very against the design so I would think you’d need specialized skills or software much more involved and time consuming than just fitting into the intended use pattern.