If a death knight unit rolls a retreat and a heroic die, does the rune golem take one damage? From my understanding, the dice result would cause the executioner ability to come into effect. As a result, the retreat would cause a damage regardless of rune golem's immovable ability. (Immovable has been nulled by executioner. Therefore, retreat would cause a damage)

Not sure if this is right. Please correct me if i'm wrong. Thanks!

Executioner causes the target to be unable to resolve retreats, but Immovable still lets you ignore them. In your example the Rune Golem wouldn't take any damage. If the Death Knight had rolled 2 retreats and a heroic, the Rune Golem would ignore 1 of the retreats, then suffer 1 damage from the remaining one.