A Death Save is, in fact, a save so bonuses to "all saves" apply to them as well. Just like a Monk gaining proficiency in "all saves" means they apply their proficiency bonus to Death Saves as well starting at Level 14.
The intent of the wording for Death Saves seems to make them special but it is only in the fact that your proficiency bonus is not added nor are they tied to a specific ability. No class starts at 1st level with proficiency in Death Saves. Monks gain it much later. Other bonuses applying to all saves such as the Paladin's ability and Rings/Cloaks of Protection will apply to them as normal.
PHB p. 197 says:
You are in the hands of fate now, aided only by spells and features
that improve your chances of succeeding on a saving throw.
Normally, a natural 1 is not a failure for a saving throw however the more specific verbiage for Death Saves trumps this. So even if you somehow have a +9 to Death Saves you will still suffer 2 failures unless you have some other mitigating factor such as something that automatically stabilizes you.
All of this intent is substantiated by Jeremy Crawford (thanks @NautArch):
Aura of Protection benefits saving throws. A death saving throw is a
saving throw.
The wizard dies - probably.
This is a difficult situation because there's no real specification of what exactly Death Ward covers when you target the "self". For all intents and purposes a creature is both simultaneously a body and a soul as a single unit, and only specifies each part when they are split.
My argument then, would be that Death Ward, when cast in this fashion, only exists so long as the soul and the new body are combined, as that is the "creature" the spell was cast on.
Order of operations:
- Cast Magic Jar, creature separates into "soul A" and "body A"
- "Soul A" possesses new "body B"
- Cast Death Ward on new creature ("Soul A" + "body B")
- Kill "Body A" or move 100' away.
- Break jar. "Soul A" is removed from "Body B". "Soul B" and "Body B" die as they cannot reunite. Death Ward dissipates as the creature that it was cast on no longer exists (but did not die).
- "Soul A" dies as it is unable to return to "Body A"
Breaking the jar is not the trigger that causes instant death (even though the soul would immediately die) thus I would argue Death Ward does not activate. The soul then dies as it specifically was not protected by the spell.
However
If you specified that the spell was cast on the soul, it might postpone your death by 1 round as the soul continues to exist in some form of limbo but the end result will be the same.
This is debatable and will likely fall under DM jurisdiction if they consider the Soul to essentially always be the target of spells such as this - the soul is truly who the creature is. The Soul however cannot survive without a host.
Additional options (DM approval) could be some form of permanent limbo that requires outside help to escape, or continuing to exist in an undead state like a ghost or specter. But these options are not strictly RAW.
Best Answer
Death Ward only triggers when you hit 0 HP (or are subject to an effect that would kill you without any damage)
The description of the Death Ward spell reads (emphasis mine):
Death Ward does not reduce the damage you take, it just triggers after you took the damage and would end up at 0 HP.
Since you still took 20 damage, the attacker would be subject to 10 radiant damage in retribution.