Personally, I consider both the cover and the screen protector necessary for the Note if you are going to be traveling about with it. The cover helps protect the Note from other objects in a bag pressing against the screen and potentially damaging it. The protector protects the screen from scratches when using the stylus.
When the Note first came out, a number of people commented about scratches on their screens from using the stylus. This was similar to the same issue with the Max2. Consequently, Onyx apparently started including a free screen protector with new purchases of the Note.
Because it is a large surface area, and because of the recessed screen, applying the screen protector can be difficult. Some people have gone to places like Mobile Outfitters to have it applied by professionals and have reported good results.
I applied mine myself. My first attempt was a disaster. Luckily, I had bought several of the protectors anticipating this. My second try went better. Just a few bubbles from tiny specks of dust. Guess the room I was doing it in was dustier than I imagined. I considered trying again, but then thought better. The little bubbles don't affect reading, writing or drawing on the screen. I can live with a few small bubbles and will keep my final screen protector for when I eventually have to replace it.
Below is a link to a YouTube video which another user posted about how to apply the screen protector. Best of luck.
https://www.youtube.com/watch?v=-96y2YbQ1NQ