Yes, animated objects have hardness.
As you linked, this situation calls for the animated object rules to be used because...
... any object can become animated, most commonly via the spell
animate objects. Permanent animated objects can be built using the
Craft Construct feat.
Which seems to cover your situation.
Instead, Animated Objects have construct traits, although they retain hardness instead of having damage reduction as per their stat block.
Constructs are immune to death effects, disease, mind-affecting
effects (charms, compulsions, phantasms, patterns, and morale
effects), necromancy effects, paralysis, poison, sleep, stun, and any
effect that requires a Fortitude save (unless the effect also works on
objects, or is harmless). Constructs are not subject to nonlethal
damage, ability damage, ability drain, fatigue, exhaustion, or energy
drain. Constructs are not at risk of death from massive damage.
No, the other rules for objects don't apply to them. Animated objects are distinct from 'inanimate objects' and I can't see that the standard object damage rules would be used. For example you wouldn't be able to Sunder or Break them.