The Perfection of Nihilism: Whenever an opposing character is KO'd, heal Thanos of 1 damage. Modify Thanos' combat values by +1 for each opposing character KO'd since the end of your last turn.

Avatar of Death: Other characters can't be healed.

How long do the effects of Avatar of Death last? If Thanos is KO'd, can other character heal?
The effects will end if Thanos is not on the map. So, yes, if Thanos is KO'd, captured, or any other effect removes him from the map, other character could heal.

Can Thanos be healed? What about his teammates?
Avatar of Death specifically prevents OTHER characters from being healed. Thanos is not an other character, so he can heal normally. Other characters could even use Support on him, if you wished.

However, since it doesn't say other OPPOSING characters, this trait will prevent his friends from healing.