The Photos/iCloud Photo Library does not work on the principle of deleting photos from your device once they are uploaded to iCloud. The way it works to conserve storage is to "optimize" your local library size. This means that although all images are "accessible" and "visible" on your iPhone, most will be just tiny thumbnails, with only some stored at larger sizes (usually the most recent ones, favorits, and those you recently topped to see at screen size). In other words, the library size is managed dynamically - if you have a lot of free storage it will keep more large sized-images; if you need the storage for other things, the local library size will be reduced.
The other - very critical to understand - part of the Photos/iCloud Photo Library use it that everything will be synced with everything else. If you Edit a picture on one device or computer, the edits will be almost-instantly reflected on all your other devices. This includes Deleting. If you delete a photo anywhere, it is deleted everywhere, so be careful. To avoid an irreversible "accidental" deletions, Apple added a Recently Deleted album, where the deleted items will remain for 30 days before being forever trashed. Just in case you change your mind....
Your current issues result from how complicated and unpredictable it is to manage what's where using iPhoto and iCloud (note this is not iCloud Photo Library) sharing/syncing works. Also note that syncing via iTunes does not actually download and backup images. For that you need to import your images to iPhoto. The images that are synced between iPhone and iCloud are those in the camera roll and My Photo Stream, which are limited to 1000 images or 30 days old, whichever is larger. I know, very complicated, hence my recommendation to switch to Photos and iCloud Photo Like Barry, unless your library is so large that it requires additional storage capacity that you can't afford.
You can read more about iCloud Photo LibraryLibrary here:
iMore has a very detailed, well illustrated article on iCloud Photo Library: