It has been well explained here how to delete photos from a device without deleting them in iCloud. However, if you want to use the same (now empty) device to upload your future photos to iCloud, you have to sync it with iPhoto again. The problem is, as soon as you sync it, not only will the future photos be uploaded to the cloud, but your old photos will get downloaded again to the device you emptied. Is there no way to automatically upload photos to iCloud without synching them?
If you have iCloud Photo Library turned on on your device, it will sync all pictures on that library. You can use "optimize storage" if you need to free space on your device.
If you only want to have your new pictures on your phone and your whole library on iCloud, you need to transfer the pictures to Photos.app manually and then upload to iCloud from there.
No. iCloud is a syncing system, not an offline/cloud backup storage system.
It's designed to allow you access to your files from any device logged-into that iCloud account. It's an all-or-nothing system.
If you want a selective-file backup system, you need to use something like Dropbox or OneDrive.