Spell description for reference
It seems clear that this spell gives objects a mode of movement which
they didn't have before. What kind of movement does it give? Can
objects walk, slide, roll, fly, etc.? What if the object doesn't have
By default, It will have a land movement. How this movement is executed will depend on his alotment of mobile parts. If the original object has no moving parts, it will achieve mobility by other means. You can look to the stone golem as a exaple, as it is created from a statue sculpted from a single block of stone, and yet it gains mobility (and joints) after it is animated. Also, you can add other movement modes when deciding its characteristics.
Do animated objects act independently of the caster? I assume so,
since otherwise, the spell would say something about requiring
concentration. Are they treated like summoned animals - attacking
enemies and/or obeying orders if possible? Can they refuse the will of
the caster - do they avoid placing themselves in suicidal (?)
How do animated objects determine the enemy so that they
can attack? Do they have blindsight or some similar ability? How far
does it extend? Do they simply divine where they need to go? If so,
are there any limits to their ability to divine locations?
The caster select a target at the moment of casting and the objects will attack it to the best of their ability. The caster can change the target as a move action, but has otherwise no other form of control over them. It is detailed in the spell description.
Also, they are treated as summoned monsters, of the construct type, obeying all orders without questions, even suicidal ones. Note that constructs have no self-will, and no life to worry about. Also, they have no intelligence, so they can only understand very basic commands. In this spell case, the orders available are smash that! and smash that other! and nothing else.
Can animated objects be debuffed in any meaningful way? Can they
acquire status conditions aside from "broken" and the like (i.e.,
conditions that apply specifically to objects)?
Animated objects cannot gain the broken status because they are considered constructs, and thus creatures, rather than items. They can be debuffed, disabled or impaired the same way any you can do with any other creature, just remember that constructs have their own set of inmunities and resistances (read this for more info). Note also that animated objects created with the spell are vulnerable to dispelling and antimagic.
How are attack and damage determined for animated objects? Is it
related to the caster level, ability modifier, etc.? Can animated
objects do anything but move, attack and full attack? When full
attacking, do objects get iterative attacks?
The link given by Wyrmwood shows the stat block of a medium sized animated object, and its many options. Depending on those options, and after size changes, if applicable (see here), you will have animated object with different characteristics, that may include multiple attacks. Increasing caster level do not advance the creatures, it allows you to animate more of them, or animate bigger ones.