How does Energy Field interact with effects that say you lose life?
In both cases Energy Field does nothing because both Hissing Miasma and Tainted Remedy cause loss of life and not damage, so Energy Field can't prevent it.
Damage to players causes them to lose life (assuming the source doesn't have infect), but loss of life isn't always damage.

118.2. Damage dealt to a player normally causes that player to lose that much life. See rule 119.3.
118.3. If an effect causes a player to gain life or lose life, that player’s life total is adjusted accordingly.