I want to free up iCloud storage by deleting photos that are backed up elsewhere. How can I delete photos from iCloud without deleting them from my iPhone?
This is possible by opening the Settings.app on your iPhone, scrolling down, and selecting "iCloud". Scroll down, then tap Storage & Backup -> Manage Storage -> [Your iPhone Name] (This iPhone). You will then see a list of all the apps that are storing data in iCloud. Chances are the top one will be "Camera" and you can switch that off. Doing that will delete photos from iCloud, and if you were to ever restore your phone, photos would not be restored. However, it will not delete the photos that are on your device already.
Also, it is important to note that iCloud Shared photos, as well as your Photostream do not count toward your iCloud backup storage limit. There is an arbitrary limit of 1,000 photos on your Photostream. You can safely leave those on without affecting your storage use amount.