If I delete a photo on ICloud from both my photos and the 'recently deleted' folder, can it still be recovered? Does Apple still save the image(s) somewhere for an undisclosed period of time, or once it's deleted, it's gone everywhere for good? Thanks.
No. Apple only holds photos for limited time in deleted items. That is your chance to reconsider. You could open a case with support to confirm, but the place to get these is from local backups. iCloud isn’t a backup just like files on your devices aren’t a backup. 

So sorry if this wasn’t your expected answer. It’s never good to lose data or learn you didn’t have backups.