CMF1_hacker* Hey CMF1_hacker!
You clearly captured the working proximity sensor of your phone there. 😉
You can safely remove the pre-applied screen protectors by just peeling it off at one of the four corners and then just remove easily by lifting it off the glass.
What you said is true, sometimes not all glass screens are 100% flat. For example my old BlackBerry Q10 was slightly shallower on the upper right and even after trying four different tempered glass protectors, I couldn't find one which would truly stick on that area, so I went with a standard film protector.
Which one to use is purely up to you, I usually prefer tempered glass to keep the genuine feel of glass, however at least for NP3 I have yet to find a really good one, so I ended up trying and really liking a matte hybrid flexible glass screen protector.