Does deleting my backup on my iPhone give me more space? I'm running out of space on my iCloud and my storage in general. If I delete my backup, will I gain more space for pictures?
If you disable/delete iCloud backups of your iOS device, it will indeed free up space in your iCloud account. This only means you will have more space available in the cloud, not on the actual device. 

If you have iCloud Photo Library enabled, note that your iCloud backups will not include that media since it’s already being uploaded to the cloud.

To free up space on your actual iOS device (again, assuming iCloud Photo Library is enabled), make sure that Settings &gt; iCloud &gt; Photos &gt; Optimize Storage is selected.