Can I delete photos in my phone but keep them in my iCloud?

If you sync with iCloud, deleting a photon on any connected device deletes it everywhere. You can turn off include sync for the device (but you'll lose functionality, like uploading images to the cloud) at Settings > Photos.

Yes, just go to settings-your name-iCloud-iCloud Photos and enable Optimize storage. This will keep a small copy on the device, but the full files in iCloud.