(Doh! Caught by necromancy yet again. I always fall for this. Never think to check the dates)
Whatever the OP prefers.
Personally, I'd go with yes, undead generally are affected by any attacks as normal, unless specified otherwise. With case-by-case basis to account for DM's whim.
By your reasoning, the cockatrice stops the stone golem by... petrifying it? Some of the consequences of this interpretation are just too wierd for me.
I don't see why not (based on my own reasoning, mind you); cockatrice turns you to unmoving stone, not the "living" stone that comprises stone golems. Again, DM preference, but personally I'd rule that yes, petrification works just fine on stone golems, earth elemental type creatures, etc.
Nowhere in the description of the Cockatrice's attack does it make mention of the fact that it affects objects at all. Therefore, the effect does not affect undead, nor does it affect constructs, IMC.
Again, DM preference. I think of anything that moves under its own power (including animated objects) as no longer being in the "object" category, in game terms. If it can move and attack, it's a "creature" in game terms, IMO. Or, if it's subject to the rules for attacks against objects, it's an object. If it's got saving throws and hit points and a MM (or spell) entry, it's a creature.