Hello,
You can check the status of iCloud Photos in Settings > iCloud > Photos. As long as Photo Stream and/or Photo Library are turned on, photos will be stored in iCloud, but they are kept in sync with your devices. This means that when a photo is deleted in one location, it will delete everywhere, including the cloud.
The way around this would be to store the photos you want off your phone somewhere else before you delete them. For example, using only your iPhone, you could select these photos and send them to Dropbox first.
If you would really like them to be in iCloud, yet not on your devices, I believe you will need some sort of computer that is hooked to your iCloud account, because I have not found a way to add photos through the built-in iCloud Drive app in iOS 9. If you have a Mac, simply sign in to iCloud in System Preferences. If you have a Windows computer, check out the official iCloud for Windows. Then, you can drag any photos you want from Photos (on a Mac) or the Photo Library folder in Windows Explorer into some other folder for storage on your computer. If you drag these photos into a manually created iCloud Drive subfolder, they should not delete when you delete them from your iPhone, but reside in iCloud, accessible from the iCloud Drive app on your iPhone, if you have iOS 9.