The sleeping opponent is considered a helpless defender and thus 0 Dex, receives no dex bonuses and is -5 to flatfooted AC. Does the defender ALSO suffer a -4 to AC for being prone?
Yes, sort of. Here's what the Helpess rule says:
A helpless target is treated as having a Dexterity of 0 (-5 modifier).
Melee attacks against a helpless target get a +4 bonus (equivalent to
attacking a prone target).
Why did they flip the wording here from a -4 AC to a +4 on the attack? I don't know. They're basically the same thing, and the rule even mentions it's an equivalent bonus. That means you don't impose both this one and the Prone one.
Rules Compendium actually changed this wording so that it's a -4 to AC instead of +4 on the attack, which is identical to Prone.
Can the shadow do a full round "Coup De Grace" on such an opponent? The question revolves around the term "melee weapon" for unarmed monsters. Are unarmed melee attackers considered "armed" when using natural touch weapons.
Here's what Coup de Grace says (Rules Compendium, emphasis mine):
As a full-round action that provokes attacks of opportunity, you can
use a melee weapon to deliver a coup de grace to a helpless defender.
You can instead use a bow or crossbow, provided you’re adjacent to the
target.
Here it says "melee weapon". Are natural weapons considered melee weapons? See below for a wall of text on that, but I say "yes". Based on that, a Shadow can deliver a coup de grace. (If your DM rules the other way that natural weapons aren't "melee weapons", then the Shadow can't deliver one.)
The ability damage would be doubled, since coup de grace is considered a critical hit:
This attack damages an opponent’s ability score. The creature’s
descriptive text gives the ability and the amount of damage. If an
attack that causes ability damage scores a critical hit, it deals
twice the indicated amount of damage (if the damage is expressed as a
die range, roll two dice).
As for the Fort save... this is all that coup de grace says:
If the defender survives the damage, it must succeed on a Fortitude
save (DC 10 + damage dealt) or die.
It doesn't really cover anything explicit for ability damage, so if you just treat it as a type of damage you should make the roll. It's at least not unreasonable int his case, since the Shadow's attack can be lethal (if you get to 0 STR it kills you).
Are Natural Weapons Melee Weapons
This is where it gets weird. First off, the Rules Compendium (p.64) says this about incorporeal attacks:
An incorporeal touch attack isn’t the same as a melee touch attack—
armor can work against an incorporeal touch attack if the armor has
the ghost touch property.
Going by that, "incorporeal touch" is not the same as "melee touch". It's actually more like "incorporeal natural weapon". From the same rule is this:
Nonmagical attacks made by an incorporeal creature with a melee weapon
have no effect on corporeal targets, and any melee attack an
incorporeal creature makes with a magic weapon against a corporeal
target has a 50% miss chance, except for attacks it makes with a ghost
touch weapon, which are made normally (no miss chance). If an
incorporeal creature throws a thrown weapon or a shoots a ranged
weapon, the projectile becomes corporeal as soon as it’s thrown or fired, and thus can affect a corporeal target normally (no miss chance).
So, we don't treat an incorporeal creature's natural weapons the same way we would treat it's attack if it was using a sword. Notice there's a distinction here on "melee weapon". That's important.
Natural weapon attacks are considered armed. If it wasn't, the Shadow would provoke an AoO anytime it tried to attack.
A creature making a melee attack with a natural weapon is considered
armed and does not provoke attacks of opportunity.
The trouble is surrounding the term "melee weapon". As we've seen, "melee weapon" can be used to refer specifically to a separate weapon that the creature is using to strike into melee (ie: a sword), and not a natural weapon being used to strike into melee. You can see other examples like this one from the Rules Compendium, for the basic standard action attack:
With a melee weapon, a natural weapon, or even a bare fist, you can
strike any opponent within reach, which is normally 5 feet for Small
and Medium creatures.
Are melee weapon and natural weapon listed separately because they're distinct things, or just because they're trying to be inclusive in what's supposed to use the attack rules that follow? "Melee Weapon" is actually a term from the equipment list, to make it distinct from ranged weapons:
Melee weapons are used for making melee attacks, though some of them can be thrown as well. Ranged weapons are thrown weapons or projectile weapons that are not effective in melee.
Obvious, right? Natural weapons are also used to make melee attacks, but nowhere in the rules will you find the phrase "natural weapons are melee weapons".
Is that distinction important? In other cases they use the term "manufactured weapon" instead, like the Monk's unarmed strike:
A monk’s unarmed strike is treated both as a manufactured weapon and a
natural weapon for the purpose of spells and effects that enhance or
improve either manufactured weapons or natural weapons.
Monks are a great example, because their unarmed strike doesn't say it's a "melee weapon", it says its a "manufactured weapon". Monks are mentioned specifically in the combat rules:
Sometimes a character’s or creature’s unarmed attack counts as an
armed attack. A monk, a character with the Improved Unarmed Strike
feat, a spellcaster delivering a touch attack spell, and a creature
with natural physical weapons all count as being armed.
So... what does all that mean? By a very strict RAW reading, you could argue that no, natural weapons are not melee weapons.
But that raises additional weirdness, because in that case a Dragon can never coup de grace. Does that make a lot of sense, considering that we're talking about highly intelligent apex predators? On top of that, a Monk could also never coup de grace with her unarmed strike, even though it's considered "armed" and does lethal damage. Yet if you hand that Monk (or Dragon) a sufficiently pointy stick, now they can? It also means that you have a bunch of weapons that are used to attack in melee and considered weapons (they do lethal damage and the user is considered armed) but are not counted as "melee weapons".
Because of all that, I believe that "melee weapon" means "weapon that makes melee attacks", which includes natural weapons. That's also the most natural way to read "melee weapon" in normal English, with "manufactured weapon" being different than "natural weapon" in this regard.