First, although the smaller scoring zone is not within a protected zone, are those cubes protected from descoring?
As you quoted, case F explicitly refers to Cubes within the opponent's Protected Zone. Descoring Cubes in the non-Protected Goal Zone is covered by case B, quoted here for reference:
B - Contact any Scored Cubes in either of opposing Alliance’s Goal Zones.
Minor violations of points A, B, C, or D that do not affect the Match will result in a warning. Match Affecting offenses will result in a Disqualification. Teams that receive multiple warnings may also receive a Disqualification at the Head Referee’s discretion.
Hopefully this answers your question. If not, please feel free to re-phrase and re-submit.
Secondly, does the interaction between a robot and the cubes need to be direct? For example, would a robot that hits the field perimeter be in violation, and thus disqualified, if the contact with the field wall causes a stack to fall.
Let's look at the full text of SG3, quoted here for reference and bolded for emphasis:
<SG3> Stay away from your opponent’s protected areas. Robots may not intentionally or accidentally, directly or indirectly, perform the following actions:
Thus, indirect contact, such as transitively through a Field Element, would still be considered a violation.