Their actions in order:
- Evangelize Belief - This allows you to add in extra Tenets to your Religion (on top of your Pantheon and Religion bonuses)
- Launch Inquisition - Allows Inquisitors to be recruited, who can remove the presence of other religions.
- Spread Religion - Like Missionaries, Apostles can spread religion. They have a chance for promotions that make them better at it, however.
To heal:
Move the apostle onto, or next to a holy site, and let them wait/sleep a turn.