Storing photos in the phone is unwise, because if the phone fails, the photos may be lost; and because they use storage unnecessarily. If you save them to Google Photos, they're safe, and you can can then Delete From Device to free storage.
There are other storage apps and I don't know which is best.
If you want to access your photos on Facebook, then they MUST be uploaded to Facebook. You can not log into Facebook from another device and see the photos on your current phone. In fact, no info stored on your phone is visible to anyone or anything else unless you specifically transfer that info (hacking being the lone exception).