Is it possible to make an enemy know whether it is poisoned or stunned so it can heal itself?

No, it is not currently possible to make an enemy respond to being poisoned or stunned. Enemy AI is limited to very simplistic conditions such as "Is weak" and "Is alone". The best that you can probably do for now is give an enemy's poison-healing attack a Prefer setting of "weakest" and a Weak/Strong stat of "poison register" so that it won't try to heal a healthy ally if it's poisoned.

It might be possible to add additional enemy AI conditions like "Is poisoned" in the future.