...turn a stone golem into a flesh golem, but an ordinary statue would become a corpse...
Is this corpse a creature?
No. 'Creature' isn't something that's really well defined in D&D 3.5, but it seems to be a catch-all term for Monsters, Humans, Undead, Constructs and anything else that walks, flies or crawls about while trying to murder player characters.
A corpse is just the body of a dead creature as evidenced by the animate dead spell.
Targets: One or more corpses touched
This spell turns the bones or bodies of dead creatures into undead skeletons or zombies that follow your spoken commands.
It's clear that this spell treats "corpses" and "bodies of a dead creature" as being synonymous. A corpse is an ex-creature, but not a creature in its own right.
Can this statue-corpse be raised from the dead, via raise dead or other means? If so, what would it be?
No. Raise dead is used to "restore life to a deceased creature" whereas this corpse was never alive in the first place, even though it is the corpse of a creature.
In addition, the subject’s soul must be free and willing to return.
The complication is that there would never have been a soul (a rather ill-defined concept in D&D 3.5) associated with the corpse, due to the lack of ever having been alive, so there is nothing that can return to the body.
Any similar spells (such as resurrection) which attempt to restore life to this corpse would also fail for the same reason. There is simply no life to return to it as it isn't the corpse of something that had actually 'died' at any point.
Can the flesh to stone statue-corpse be the target of animate dead?
Yes! Animate Dead and similar spells doesn't care about pointless things like souls, all it needs is the raw material of a corpse or a skeleton - for which our statuesque friend should be ideal.
This answer approaches what appears obvious from another direction. Disagreements with conclusions are welcome, but the answer seeks to accommodate—not prove or disprove—different readings. I think any campaign can be run just fine relying exclusively on Phlyk's fine answer, but the D&D 3.5 game is vast, unwieldly, and often contradictory, so there's room, I think, for some nuance. The author hopes that some of the ideas and information is useful even if you disagree.
Maybe the corpse that results from a statue targeted by the spell stone to flesh is a creature (or, at least, a dead creature)
The D&D universe is broken into at least two broad categories: creatures and objects. (Edge cases—energy, for example, and actual foliage and intelligent magic items—notwithstanding.). The Monster Manual says, "Anything that lacks Wisdom or Charisma is an object, not a creature" (298), and the Player's Handbook mentions nothing about a creature's ability scores becoming nonabilities when a creature has the condition dead (307). So, yeah, it's fairly safe to say that a corpse is a creature with the condition dead. However, the FAQ disagrees and declares a corpse an object. Ask the DM which he prefers or, even, if it's an edge case therefore both.
Maybe such a corpse can be targeted by the spell raise dead et al.
My initial reaction to this query was the same as this answer: No. The corpse was never alive so there's no soul to return.
However, there's also no mention of how souls are gained in D&D 3.5. I mean, there are discussions of souls (such as in Magic of Incarnum) and adventures involving souls (the on-the-nose Bastion of Broken Souls) and even ways to (presumably, anyway) give soulless creatures souls (e.g. the 9th-level Sor/Wiz spell incarnate construct [trans] (Savage Species 67-8)), but the game puts no hard-and-fast numbers in core as to when or, for that matter, under what circumstances any creature naturally acquires a soul that's then fixed to its body.
Thus, if the DM says that souls exist somewhere independent of bodies and wait to be assigned to a living creatures (as opposed to nonliving creatures—constructs, undead, and the like—, not as opposed to dead creatures), when a new appropriate creature is created, a soul could be assigned to the creature, and it shouldn't really matter if the living creature is alive or dead at the time. I guess it might kind of suck to be assigned to a newly created dead living creature, but maybe where souls hang out before they've been ensouled is awesome, filled with video games and candy? Anyway, let's assume they don't know what they're missing and not feel bad for them.
Upon reflection, I'm not entirely sure there is an alternative to this. It's possible instead that a body creates a soul, but that still leaves the resultant corpse from casting the spell stone to flesh on a statue with a possible soul. The DM could decree that a living creature must undergo whatever kind of birth is conventional for the creature to earn a soul, and that seems reasonable, but it might be a bit closed-minded. Reproduction by stabbing an egg into a dude and having the egg-essence transform the dude into a whole new creature, for example, makes a mockery of conventional, after all.
So ask the DM. Even this player would be satisfied with a simple No because it didn't have a soul in the first place, but you could (ahem) raise the idea right before casting raise dead on a former-statue-that's-now-a-corpse just to give the DM pause. And whether the raise dead spell succeeds or fails, you've learned something about the universe that might be important later.
Maybe such a corpse can be targeted by the spells animate dead and create undead et al.
Again, my initial reaction was identical to this answer: Sure. Parts is parts. The undead don't care.
But the Player's Handbook says that a creature possessing the type undead must first be destroyed before the original creature whence it came can be the subject of the spell raise dead et al. However, this is contradicted by the description of the type undead in the Monster Manual, it saying, "Resurrection and true resurrection can affect undead creatures. These spells turn undead creatures back into the living creatures they were before becoming undead" (317).
Either way, there is a connection between the malevolent force that provides unlife to a corpse, the soul, and the body. That connection's strength and meaning will depend on the DM. It's possible (although it may seem weird) for a DM to rule that undead creatures can result only from dead living creatures that once possessed souls, that a totally empty shell—only a body and having never had a soul—just can't sustain a malevolent force. This makes attempts at upbeat necromancy impossible: An undead creature's malevolent force needs to have a soul's remnant in the body with it for the creature's animation to continue.
An aside: Atrocity exhibition
I've avoided delving too deeply into splatbooks because they make thing even more confusing, but Libris Mortis on Manifestations of Death says
One unifying element defines most undead creatures: Each must have been alive in the past, no matter how little of the original creature is left, even if just the spirit or memory remains. Although extreme and rare cases have seen small bits of the energy of unlife itself (negative energy) take on terrible form and purpose, almost all undead once had breath in their bodies before gaining their feared title. (5)
This, then, makes animating a formerly-stone-statue-now-a-corpse usually impossible, but the core rules remain silent on such a situation. The DM must determine whether this changes the rules or merely extends them.
So if the malevolent force needs to, essentially, torture the body's soul to continue its unlife, that's horrifying… and kind of spiffy narratively. Yet it does limit the power-hungry necromancer from commissioning sculptures of wacky imaginary beasts, casting on them the spell stone to flesh then casting on them animate dead or whatever to get wacky imaginary zombie beasts. Both perspectives make good story fuel.