1) It is a coat. The line "You can use this coat" covers that for me. 2) and 3) Its possible that it falls in between, but see below.

• Common terms states:

  Bonus (Armor)

  An armor bonus applies to Armor Class and is granted by armor or by a spell or magical effect that mimics armor. {snip}

• Heavens Coat of Many Stars states:

  Coat of Many Stars (Su): You conjure a coat of starry radiance that grants you a +4 armor bonus.

• Conjuration Creation (which is just for completenes, since the effect isn't called out as any specific school) states:

  Creation: a creation spell manipulates matter to create an object or creature in the place the spellcaster designates.

From this we can determine that you are in fact wearing an item of clothing, its not just shiny lights, it is in fact an object (though don't ask me how you sunder it), and furthermore, it is specifically called out as clothing (coat).

Magic Vestment states:

An outfit of regular clothing counts as armor that grants no AC bonus for the purpose of this spell.

I would argue that "regular" in this case means "not armor", rather than "commonplace". I'm pretty sure it was not intended to a silken shirt could not have magic vestment cast upon it.

Now, either the coat is armor (because it provides an armor bonus) or it is not (and is therefore clothing). Either way the spell works.

Note: A really stingy DM could argue that clothing doesn't have an AC bonus and therefore the second part of this doesn't apply, in which case your stuck with your DMs interpretation. However, since the spell goes out of its way to basically say "armor or just whatever your wearing" I think the fact that is intended that it should include special cases that fall in between. Point out that Oracles can normally wear armor anyway, and that Mage Armor, Magic Vestment and normal clothing would work.

( All emphasis mine )

No, natural armor bonuses don't stack

A natural armor bonus

improves armor class resulting from a creature's naturally tough hide. Natural armor bonuses stack with all other bonuses to armor class (even with armor bonuses) except other natural armor bonuses. Some magical effects (such as the barkskin spell) grant an enhancement bonus to the creature's existing natural armor bonus, which has the effect of increasing the natural armor's overall bonus to armor class. A natural armor bonus doesn't apply against touch attacks.

In the case of the sorcerer's draconic bloodline power dragon resistances, the natural armor bonus increases as the sorcerer gains levels. Other natural armor bonuses less than or equal to this amount are ignored, and if the sorcerer gets a higher natural armor bonus from a source other than his dragon resistances, he'll ignore his dragon resistances natural armor bonus in favor of the newer, higher one.

For example, a creature like a kobold that begins play with a +1 natural armor bonus to Armor Class and that is also a Sor3 still has but a +1 natural armor bonus to Armor Class (the natural armor bonus from his race and dragon resistances overlapping) but the creature still gains other benefits of the bloodline's powers.¹ When the creature becomes a Sor9, he'll have a +2 natural armor bonus to Armor Class, his dragon resistances even more completely superseding his racial natural armor bonus to Armor Class.

¹ Keep in mind, though, that the creature does, in fact, actually have both bonuses even though both can't be used. Were the creature to lose its race (perhaps upon being the target of the spell reincarnate), dragon resistances would still apply. Were the creature to retrain its levels of sorcerer to another class, the creature would keep its racial +1 natural armor bonus to Armor Class. Having both of this race and this ability, however, means the two effects overlap.