These are resolved in the order of the player's choice! For example, if. Patches has 1 HP and Poison 1 on him, he can choose to use his innate ability to heal before taking the Poison damage. Similarly, if a Baddie with Recover 1 is in a similar situation, you can choose to apply the Poison damage before Recover so it is defeated before healing.
Use this to your advantage! Note that Fatigue occurs at the beginning of a Round, not a turn, and affects all Baddies and Gearlocs simultaneously.