You can activate “Judgment of Anubis” when there are no monsters on your opponent’s side of the field.
When you activate “Judgment of Anubis”, you destroy your opponent’s monster after the activation and the effect of the Spell Care are negated. This means that the monster-destroying effect of “Judgment of Anubis” does not target.
You can activate “Judgment of Anubis” and select a Spell Card that destroys only a Spell Card (like “De-Spell”) or only a Trap Card (like “Remove Trap”) or could destroy both (like “Mystical Space Typhoon”) or many (like “Heavy Storm”).
You can activate “Judgment of Anubis” and select a Spell Card that negates the activation of a card and destroys it, like “My Body as a Shield” or “Bait Doll”.
You cannot activate “Barrel Behind the Door” against “Judgment of Anubis” because when “Judgment of Anubis” is activated, it has not been confirmed that the damage-inflicting effect will happen.