By (2), are you referring to the fact that you don't have to refocus your eyes when shifting your view between objects at different distances?
I've never tried one, but I'd assume the screen is projected at infinity or close to? This should only be an issue with objects that are closer than 1.5ft or something.
Yes, it's only a problem with objects that are unusually close to your face. It's a small concern and only really relevant for people designing VR content, because with properly designed content users should never notice.