Q.258, some questions about Abjurers

A. If an Abjurer learnt the Armor of Agathys spell, would their arcane ward or their temporary hit points be the first to be lost?

B. If the ward tanks the damage, would the retaliation damage from AoA still trigger?

C. If a level 18 Wizard chose an Abjuration spell as their Spell Mastery option, can they spend a few out of combat rounds to reset their Arcane Ward to max HP at will?