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.
The chains have no speed
Abilities do only what they say they do
In 5e, spells and abilities do only what they say they do. If the ability gave the chains a speed, it would have said so in the line detailing the chains' statistics.
Each animated chain is an object with AC 20, 20 hit points, resistance to piercing damage, and immunity to psychic and thunder damage.
Not only does the ability not give the chains a speed, but the chains are also explicitly defined as objects. An object does not have a speed unless an effect of ability explicitly gives one to it.
Compare to animate objects
For example, compare the wording of this ability to the spell animate objects:
An animated object is a construct with [list of statistics]. Its speed is 30 feet; if the object lacks legs or other appendages it can use for locomotion, it instead has a flying speed of 30 feet and can hover. If the object is securely attached to a surface or a larger object, such as a chain bolted to a wall, its speed is 0.
Notice even an intelligent construct, a creature, (which the chains are not) is required to specifically have a speed given to them.
The ability is lacking much more information than just the numerical speed
Not only does the ability not list a speed but it also lacks a description of how the chain would move (crawling? flying?) and how they would decide where to go. Remember, these chains do not have any form of intelligence or any kind of sight. So, how could the chains have the capability to even decide where to move?
Also note that the Chain Devil is not granted the ability to command the chains to do anything except attack and grapple (which aren't even commands so much as automatic things that happen under the listed conditions). Even if the Chain Devil tried to command them, the chains have no ears or any capacity to understand speech.
The chains are simply objects that are able to make attacks and grapple when the Chain Devil meets the listed conditions. There is no reason to assume that the intent was to give them a speed and, in fact, the lack of key information needed for this to be possible is a decent indicator that this was not the intent. Thus, the chains have no speed.
Note: Having no speed and having 0 speed are mechanically different. Something with no speed cannot move unless something gives it a speed. Something with 0 speed could move once the 0 speed condition is alleviated or if they are able to get a bonus to speed that would increase it above 0. (thanks @DavidCoffron)
Best Answer
So far as I know, animated objects are the result of an animated object spell, nothing else. Hiring an NPC to cast animate objects and then permanency would cost 16,540 gp minimum (caster level 14th for the casting of permanency on animate object; at that CL you could get a Huge one).
Crafting a Construct by the Craft Construct rules would result in a creature not vulnerable, as a permanent animate object is, to dispel magic, which is a rather huge advantage. On the other hand, it takes longer to set up (the whole crafting time), not to mention the Craft Construct feat itself, so it perhaps makes more sense to compare it to other Constructs that you can craft. It’s better than a Flesh Golem (20,000 gp) most likely, but not as good as a Clay Golem (40,000 gp). I’d probably put it around 25,000 gp then, base cost.