Companions can rest, even if they have full health, however don't forget only one survivor can rest per round, which includes companions!
If the SPECIAL ABILITY side of the die is rolled, unless it's during a round of combat that the enemy will be defeated in, the ability automatically activates.
When the SPECIAL ABILITY is rolled, even if in the middle of combat, all survivors can choose to gain a health or draw an item at that point, which could even be a health item!
The Spirits' 5 actions are only used up when either leading into a chapterdrawing an item or rolling her die.