Is an abjurer’s Arcane Ward healed only when the ward has 0 hit points? The ward regains hit points whenever the abjurer casts an abjuration spell of 1st level or higher, not just when the ward has 0 hit points. As is normal for healing, the ward can’t regain more hit points than its hit point maximum: twice the wizard’s level + the wizard’s Intelligence modifier.
Does casting alarm as a ritual heal Arcane Ward? Any abjuration spell of 1st level or higher cast by an abjurer, including a ritual, can restore hit points to the abjurer’s Arcane Ward.
How does Arcane Ward interact with temporary hit points and damage resistance that an abjurer might have? An Arcane Ward is not an extension of the wizard who creates it. It is a magical effect with its own hit points. Any temporary hit points, immunities, or resistances that the wizard has don’t apply to the ward.
The ward takes damage first. Any leftover damage is taken by the wizard and goes through the following game elements in order: (1) any relevant damage immunity, (2) any relevant damage resistance, (3) any temporary hit points, and (4) real hit points.
An abjurer gains resistance to spell damage at 14th level. Does the abjurer’s Arcane Ward gain this resistance when a spell hits the abjurer? The abjurer, not the Arcane Ward, gains the resistance at 14th level.
Sage Advice Compendium, v2.7 r2021