iCloud photos

If you have iCloud Photos turned on, the photos in iCloud are also on your device. iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: https://support.apple.com/en-us/HT204264

Apple does not currently offer cloud-only storage for photos. If that is what you want or need, you may want to explore 3rd party options such as Google Photos or Dropbox.

Use any computer internet browser and log into www.icloud.com and go to the Photos app there and click on Photos in the sidebar. The total number of photos is displayed at the bottom of the screen.