If a combat is initiated but no combat damage occurs (because units are moved or killed by spells before the damage step), do units at other battlefields still heal?

Ruling: Yes, once combat is initiated, all steps and phases of combat occur including healing, regardless of whether combat damage is actually dealt.

Sequence:

• Combat is initiated when a unit moves into an opponent-controlled battlefield
• All combat steps and phases proceed
• Healing occurs even if no combat damage was dealt