The “skip Healing” and “prevent Conquering” abilities are resolved in the Monsters (and Ghosts) Step of Battle.

Fast spells that force you to withdraw a monster prevent it from using its ability, as does Metamorphosis (it turns a monster into a sheep with no abilities).

However, Blind Rage does not affect other abilities (it just alters the attack type), and Dimensional Gate is a slow spell, so the ability takes effect even though the monster is teleported away.