Question Mark,
So I used a lens cleaner with a microfiber cloth. So far, nothing bad happened. I don't know if various such sprays have very different formulas, the one I used is Hilco Leader Lens Cleaner in a big 236 ml (8 oz) bottle, so I have a lot of it left for further cleaning

It says on the bottle: Alcohol-FREE AR formula, effectively cleans all lens types without streaking.
Amazon says: Providing effective, streak free cleaning, Hilco's Leader lens cleaner is alcohol free and Colts approved for use on all eyewear lens coatings.
Whatever "Colts approved" is.
After cleaning the screen, I don't see any scratches yet. Perhaps not too late to put the protector on. But do I need it, if I will not be using the stylus anymore. I will not be using any swipes or dragging with fingers either, just in case. Just gentle taps. Except when selecting a multi-word phrase for a dictionary lookup.
The built-in file manager (Storage) allows to get to any place in long lists without any dragging, just by tapping page up / page down virtual buttons or tapping any point on the slider.
It is worse with Cool Reader - its built-in manager does not support that. I am thinking about modifying CR if I can manage to build it from sources. In that case I would put the page up / page down actions on the "back" button of Note. I already did that with next page/previous page buttons: next page/previous page/exit: single press/double press/long press.