A Thief's backstab absolutely stacks with sneak attack damage

Thieves are painful painful creatures, especially with the +3 to accuracy after the attack roll on backstab. Just owie. But you're talking about a scoundrel's interactions with backstab and sneak attack, which presents some complications.

Your scenario doesn't work, but not for the reasons you think

So, backstab is a thief (rogue subclass) encounter power. As a Level 3 thief, you could use a trick to gain CA as a move action, and then backstab + sneak attack two turns in a row.

As a Scoundrel Rogue (normal rogue), you can never have two backstabs. You may spend a feat to replace one of your encounter powers with backstab by taking the Thief's Backstab feat.

You seem to be conflating thief with scoundrel and cherrypicking bits from both. They are different classes, though they pull from the same lists of utilities.

Also, there are better things to do than Preparatory Shot. Many. Many. Many better things to do. (This is a public service announcement.)

The feat, backstabber improves sneak attack, not backstabbing. Ignore the word similarities and move on.

Backstabber, written 3ish years before the essentials line, was a cutesy name for a "more damage!" feat. It just makes sneak attack better. It's a great feat.

Backstab, the utility, is a utility. It isn't sneak attack. Therefore it isn't improved by things that improve sneak attack.

A basis for comparison

Since you seem to like thinking about damage, a thief cheesed for damage at level 3, as taken from here, will:

Round 1, move: use a acrobatic trick or equivalent to gain CA on a target of their choice with a move action Round 1, standard: Will charge with a vanguard rapier, and the feats surprising charge and backstabber. She will use backstab on the rare event of a miss. This charge does 1d8 (Rapier) + 1d8 (Surprising charge) + 1d8(Vanguard) + 2d8 (Sneak Attack + Backstab feat) + Dexmod + 2 (Bracers of mighty striking).

She will then continue to perform this little trick every round until she gets bored.

A rogue will have a slightly more complex time of things, but can get similar fun things going.

Prepratory shot is a trap. You really do want to be doing weapon damage. And if you actually want to do lots and lots of damage, you want to look at how charge interacts with thief.

As a scoundrel Rogue, and a bugbear, ... and apparently a scholar, if you want lots of damage:

Be a bugbear. Grab gritty sergeant background for rapier proficiency, Be a Brutal Scoundrel so you can add strength mod to all your damage rolls and so you're a Sergeant Brutal Scoundrel Scoundrel (gives you a reason to kill people when they laugh at your description). Attack with piercing strike (attack versus reflex instead of AC makes you significantly more accurate.) Gets you 1[W] (2d6) + Dex + Str + 2d8. Drop the standard "charging chassis" on top of that for extra fun.

On the nature of scoundrels and thieves.

The "essentials" line of D&D books introduced new conceptions of the standard classes. In order to differentiate them, they relabelled most of the classes. Thus, there is no longer such thing as a "Rogue" as Rogue. Instead, there are Thieves (using the rules for essentials) and there are Scoundrels (using the original PHB I rules for rogues.)

They are both considered Rogues, which is why they can take feats labelled for Rogues, and they share utility powers. But a Thief can't take "rogue" encounter powers because her class features give her the Rogue Utility: Backstab, instead. The Scoundrel can't take Backstab because it doesn't have a level: it can only be granted by a class feature.

It is not possible to "hybrid" the scoundrel and the thief. It is possible to fake it with the judicious application of feats, but just like every other hybrid it. Is. a. trap. I've never successfully built a fun and playable hybrid. I've built quite a few unplayable ones though.

When considering classes, consider first your objectives¹ and then figure out how the class features satisfy your objectives.

I cannot comment on the cosmetics of the rogue, though I understand no few of them choose to wear rouge, scoundrels and thieves alike.

¹ Brian Ballsun-stanton, Samuel Russell (2012) Constrained Optimization in Dungeons and Dragons : A Theory of Requirements Generation for Effective Character Creation.

Unarmed attacks can crit, but do not do double damage

• Can an unarmed strike crit? - Yes

  If you roll a 20 on an unarmed strike, it is considered a critical hit.

  This means that it will automatically hit regardless of the opponent's AC and has the potential to cause 2 failed death saving throws from a creature at 0 HP.

  However, a critical hit does not get to increase its damage from a critical hit.

• Do unarmed strikes get double damage on a critical hit? - No

  Critical hits only double damage that you roll. Unarmed strikes do not have any damage rolled. So, RAW, critical hits do not increase the damage of unarmed strikes. See this Q&A for further discussion of this.

  Jeremy Crawford agrees and has (unofficially) clarified:

  An unarmed strike deals 1 + Str. modifier damage, even on a critical hit.

  This ruling, besides being in line with the literal reading of the RAW, is likely made to keep the rules of what damage to multiply from a critical (only rolled damage) consistent. If you have to start carving out exceptions for every static damage effect that doesn't roll damage but you think might kind of be like a roll, applying the critical hit rule could get complicated and cumbersome. Thus the simple, easy-to-apply ruling we get here.¹

Does the described attack cause failed Death Saving Throws? - No

• It is possible for an attack to do 0 damage

  Jeremy Crawford has (unofficially) clarified:

  There is not a damage minimum of 1, so it is possible to deal 0 damage with an attack.

  So you are indeed calculated the damage for that attack correctly.

• 0 damage does not count as damage

  Jeremy Crawford has (unofficially) clarified:

  Taking 0 damage is the same as taking no damage.

• No damage means no failed death saving throws

  If an Unconscious character takes damage while at 0 HP, they automatically fail one death saving throw, or 2 death saves if the damage is from a critical hit.

  If a creature takes damage while at 0 hp, then they will fail one saving throw (or two for a crit). If no damage is taken then no death saving throws are failed. The critical does not change this because damage is a prerequisite in order for any death saving throws to be failed in this way.

So the character in this case does not fail any death saving throws as a result of the attack

^{1 - Note that I've played in and run games where I've allowed unarmed strikes to double damage as a house rule, and it seems to have had only positive effects (if any, since it came up extremely rarely). But it was always made very clear that this exception was being made for only this one thing. If you did so at your table, I'd guess you wouldn't have any issues either. The only thing to watch out for is confusion I'd say, because the rule that only rolled damage is rerolled is a handy one, and breaking that for unarmed strikes might undermine that. I've only done this house rule with experienced players, so keep that in mind.}