How do I delete something only on my device and still preserve it in cloud? I still have a very vague understadning of how iCloud Library and the new 'Photos' app operate. How do I distinguish between photos on my device and what is stored in cloud. How do I delete something only on my device and still preserve it in cloud? 

Right now I have 2215 photos and 6 videos in iCloud they say. Ok, so where are my all other videos that I was forced to delete due to insufficient space? 

I guess I can always use something different like Google Drive, Dropbox or Picasa to back it all up manually and have complete access to it all the time, but I just want to understand if Apple's new solution is completely useless.
To strictly answer your question, it is not possible to delete something from your device and have it remain and accessible from iCloud Photo Library. 

Here's more details:

The idea behind iCloud Photos Library is to have all your photos on all your devices. Picture a parent of a small family in California who takes, on average, several photos a week and has a Mac, iPad, and iPhone. When they take a photo on their iPhone, it syncs to their other two devices automatically so that when they arrive home, they can open their computer and view the photos or videos they took. Pretty cool? Yes, for some situations it's ideal. 

But there's a problem, if you don't have enough storage on your phone to hold all of the photos, iCloud Library is stuck until you open settings and allow it to optimize your device storage. It then saves low resolution photos to your device and will download the high resolution version when you view the photo. This too is convenient in some situations. 

The problem comes in when you want to control what photos go where. I've taken thousands of photos and videos on my iPhone and I don't want all of those on my phone even if I could have that. But with iCloud Library enabled, all of your photos will be on your device as there is no way to control what images are in the cloud versus on your device. So, it seems that Apple's solution to your problem of having too many photos and videos on your phone would be to enable the option to optimize device storage. 

However, here is, by far, the biggest problem with iCloud Photo Library and the "optimize device storage" option. If you enable that setting, and then go to disable it at some point, it will attempt to download the full resolution version of all your images (not just the device-optimized high-resolution one). This makes sense, but causes a problem as your device likely wouldn't have near enough storage by then to handle that. Consequently, that's probably not the approach you would want to take. 

To summarize: use iCloud Photo Library if you don't take (or keep) a lot of photos and if you have more than one Apple device. Otherwise, it's probably better to avoid it.