No, critical hits must be linked with attack rolls.
I checked with Jeremy Crawford on Twitter and he says that critical hits must come from attack rolls:
@JeremeyECrawford No, since only attack rolls can score critical hits.
In response to @Kevinaskevin Can my Rogue's Assassinate cause my Wand of Magic Missile to crit against surprised creatures?
You should read the full conversation between he and I to get more detail.
Critical hits come up in the PHB on pgs. 194 & 196. As I see it the PHB pg. 194 text doesn't imply that critical hits are exclusive to attack rolls:
If the d20 roll for an attack is a 20, the attack hits regardless of any modifiers or the target’s AC. In addition, the attack is a critical hit, as explained later in this chapter.
PHB 196 describes critical hits but never uses the words "attack roll". Reading the text above someone new to DND could reasonably assume there are other causes of critical hits.
Despite this, Jeremy made it clear that the game designers intended critical hits and attack rolls to be linked.
Death by many Magic Missiles
Let's start with when to make Death Saving Throws (PHB, 197)
If you take any damage while you have 0 hit points, you suffer a death saving throw failure.
So any time something gives you damage while at 0 hit points, you suffer a saving throw failure.
As quoted above in the question, the language for Magic Missile is separate per missile. Each missile strikes simultaneously, but the damage from each is separate. If we are separating damage, we are separating those Saving Throw failures.
The Concentration function is similar in that it triggers off of damage (PHB, 203):
Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw.
However, it also goes on to state:
If you take damage from multiple sources, such as an arrow and a dragon’s breath, you make a separate saving throw for each source of damage.
Jeremy Crawford specifically ruled on Concentration saves and Magic Missile requiring each missile to force a new save.
Roll for each missile
The real question
That leaves us the real question here as to whether or not Magic Missiles are separate sources of damage, or if the missiles hitting concurrently represent a single taking of damage.
Given that Crawford seems to believe that magic missiles are multiple sources that require a roll per source, it seems you can extrapolate that the missiles are also giving damage separately (while hitting concurrently) and thus forcing death save failures for each magic missile. The concurrent nature of the strike doesn't override the multiple deliveries of damage from separate sources.
Caveat Emptor
If you are a DM and planning to target a PC like this, you must beware of hard feelings at the table. Typically death saves are a PC thing, and if you are going to remove that by going after unconscious players then the possibility of hurt feelings is real. Most monsters are more concerned about taking out other creatures who are alive rather than double-tapping any downed creatures. If there was a real reason by the NPC to do this, then that's different - but if you're just going after unconscious players because they're easy targets to completely kill you may suffer backlash from your table.
Best Answer
This should give you 1d4+3 force damage per dart created by magic missile.
For your example, if a magic item grants 1 to spell DC, +2 spell attack rolls and +2 to spell damage, then due to its wording it would increase spell damage by 2 whenever damage from a spell is calculated. (I would rule that a non-damaging spell would not be affected since it wouldn't have a damage formula to increase or a damage type.) In this example, magic missile would deal extra damage on each dart.
Jeremy Crawford indicates in a question about Empowered Evocation which is similar that you should determine the damage for a single dart and use that for every strike. (Your DM may decide to roll each dart's damage separately, but you should still get to add all of your bonuses to each dart.)
https://twitter.com/jeremyecrawford/status/557820938402947072
In general, it depends.
Since this question started out very generically.
The exact wording of the feature that grants the extra damage is very important. If the spell has to be a hit (which requires an attack roll), sometimes a save, and sometimes it just has to deal damage, or be qualified in some other way.
The 1st level Warlock spell Hex adds an extra 1d6 necrotic damage whenever you hit with an attack. So this would not apply to saves or spells like magic missile that don't require an attack roll or a save.
Knowledge Clerics gain Potent Spellcasting at level 8, where they add their wisdom modifier to the damage of any cantrip. This would apply to any damaging spell.
Evocation Wizards gain Empowered Evocation at level 10. This feature adds their intelligence modifier to the damage of any wizard evocation spell. This would apply to any wizard evocation spell, whether it used attack rolls or saves. Magic Missile is such a spell.