Sir from your answer it seems that you haven't read what I've been posting so far.
I can just repeat:
1. once you set a menu item ACCESS=GUEST,
2. you apply any change to the menu via megamenu,
3. save megamenu configuration and then
4. save and close the Template Style.
from that moment on (clear the cache, reload) megamenu requires you to set ACCESS=GUEST to change anything in the menu, submenus and all the rest (icons, caption), for ANY menu item in that menu.
It did not work this way in J3, I checked on a demo site (JaLawFirm) as well, so I guess it's a bug.
If you're not willing to look into this, can I speak with someone else? I'd provide any detail again and do some testing if necessary.