What do the different apostle skills (Evangelise belief, Launch inquisition, Spread religion) do in Civ 6, and how can I heal them?

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, which 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.

Apostles (or either of the other two religious units) can only recover HP on (or adjacent to) Holy Sites of their Religion. Move the unit onto, or next to, a Holy Site and sleep / skip turn until they're back to full health.