[RPG] How small can a “Tiny” object be

An object is any physical thing that is not a creature:

... targets creatures, objects, or a point of origin for an area of effect...

Chapter 10. Spellcasting, pg. 204 of PHB

The above description lists creatures, objects, and points in space as the 3 distinct, mutually exclusive types of targets. Note that spell effects are not physical things, and so are not objects, creatures, or points in space, though spell effects can affect, create, or share space with one or more of them.

A creature is anything that can take any (or at least most) of the general actions. All creatures fall into the categories of either Player Character or Monster:

A monster is defined as any creature that can be interacted with and potentially fought and killed... the term also applies to humans, elves, dwarves, and other civilized folk who might be friends or rivals to the player characters.

Introduction, pg. 4 of MM

So, you can also say that anything besides the PCs that isn't covered by the MM is an object.

This means that arrows, weapons, armor, and shields are, in fact, objects. NOTE: using some objects have more specific actions, so the "Use An Object" action you quoted does not apply. This is case for arrows (ammunition property of weapons and the attack action), weapons (the attack action), and armor and shields (donning and doffing and armor class). If you do something unconventional with one of these objects, such as using a sword as a lever to crank a wheel, the "Use An Object" action would apply.

The Spell Animate Objects effectively turns 'objects' into 'creatures.'

Each target animates and becomes a creature under your control until the spell ends or until reduced to 0 hitpoints.

Creatures occupy space on a battlemap, they don't just hover in an enemy's space. In fact, they can't.

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

As these creatures are Tiny, per PHB 191, they take up a 2.5 ft x 2.5 ft space...meaning you can fit four of them into a standard 5 foot battlemap hex.

So, in dealing with this spell, you would track the location of each 'creature' created by Animate Objects separately on the battlemap, where they have a Fly speed of 30' for the purposes of moving around. If you want to make your life easier, clump them into groups of 4, and track them that way.

In essence, Animate Objects works just like a conjuration spell where you summon up a pack of wolves. They have a space they occupy just like every other creature on the map. And you determine if they were hit by a spell the same way. Technically, they should even roll their own initiative, as the spell specifies:

You decide what action the creature will take and where it will move during its next turn

Emphasis Mine (For simplicity, I personally just have them all act on the caster's turn)

As for how many attack each round? As many as all of them, assuming they are in range of a creature they can hit.

As a bonus action, you can mentally command any creature you made with this spell if the creature is within 500 feet of you (if you control multiple creatures, you can command any or all of them at the same time, issuing the same command to each one).