Thanks for stopping by the Apple Support Communities. From your post, I understand that you have some questions about how to free up storage on your iPhone. Specifically, you're wondering if you can delete pictures after running a backup. I'm happy to help!
First, take a look over What does iCloud back up? - Apple Support , which discusses what is backed up with iCloud. If you're using iCloud Photo Library, iCloud backups do not also back up your pictures--those are synced with iCloud to keep them the same across all of your device. If you delete those photos, then, it will delete from iCloud and all other devices. You can get more information on iCloud Photo Library here: iCloud Photo Library - Apple Support .
What I would recommend instead is using Optimize Storage; this feature of iCloud Photo Library will upload pictures and video as needed to free up space on your iPhone. You can get more information on this feature in the previously linked article.