[RPG] Would a very small creature inside a sealed container carried by a character take damage from AOE spells

Should rolls be made on content breakage per attempt made on the box

There is a brief description of HP for items in the DMG (and repeated in the SRD), which basically says objects have HP, when that HP is exceeded it breaks. The rule books don't have any specific rules about damage carry over.

A fair house rule where any damage beyond the chest is done to the objects (evenly dividing or most fragile first -- up to the DM). If they exhaust the objects inside, they also break.

There is also armor classes for objects (DMG 246), but if the item is immediately in front of you, and there is no threat, rolling against AC is a silly exercise, as they'll just keep rolling until they finally hit it. Object AC makes more sense if in the heat of battle (or on the run fleeing) a player wants to smash something.

Are potion bottle and scrolls generally strong enough ... ?

A fragile Chest is 3 HP, and a resilient chest is 10 HP It also suggests a fragile Potion bottle is 2 HP, and resilient bottle is 5HP.

This chart is on 247 of the DMG.

In this GM's opinion, a spell's description provides the only guidance for determining if a spell that has an Area entry that also deals damage also deals that damage to objects within that area.

That is, while Damaging Objects on Saving Throws on Attended Items does say, "Unless the descriptive text for a spell (or attack) specifies otherwise, all items carried or worn by a creature are assumed to survive a magical attack," on Unattended Items says, "Non-magical, unattended items never make saving throws. They are considered to have failed their saving throws, so they are always fully affected by spells and other attacks that allow saving throws to resist or negate," but when taken together it's unclear if this means either All items not carried or worn by a creature are assumed to be dealt damage by effects that affect an area or A spell (or attack) will specify that items not carried or worn by a creature are dealt damage by effects that affect an area.

While this answer gravitates toward All items not carried or worn by a creature are assumed to be dealt damage by effects that affect an area, in this GM's campaigns A spell (or attack) will specify that items not carried or worn by a creature are dealt damage by effects that affect an area. A reader may judge me lazy, but I just don't want to track damage to unattended objects (and have that matter) if I don't have to. I feel there are better ways for a GM to spend his time. To that end, to determine if a spell deals damage to unattended objects in its area, I use as a guideline a really strict reading of those 40-year-old standbys, the spells fireball and lightning bolt.

Bear with me here. The spell fireball says that

A fireball spell generates a searing explosion of flame that detonates with a low roar and deals 1d6 points of fire damage per caster level (maximum 10d6) to every creature within the area. Unattended objects also take this damage.… The fireball sets fire to combustibles and damages objects in the area. It can melt metals with low melting points, such as lead, gold, copper, silver, and bronze. If the damage caused to an interposing barrier shatters or breaks through it, the fireball may continue beyond the barrier if the area permits; otherwise it stops at the barrier just as any other spell effect does.

(Emphasis mine.) Similarly, the spell lightning bolt says

The lightning bolt sets fire to combustibles and damages objects in its path. It can melt metals with a low melting point, such as lead, gold, copper, silver, or bronze. If the damage caused to an interposing barrier shatters or breaks through it, the bolt may continue beyond the barrier if the spell's range permits; otherwise, it stops at the barrier just as any other spell effect does.

(Emphasis mine.) Some will be quick to point out that just because, for example, the (equally elderly) spell flame strike does not say it deals damage to unattended objects in its cylinder also does not mean it doesn't deal damage to unattended objects object in its cylinder. But, because—unlike fireball and lightning bolt—there are no specific rules for what happens to a barrier when part of a flame strike's effect intersects with it, this GM has the flame strike spell stop at the barrier just as any other spell effect does and leave the barrier undamaged. That's just how I roll. (As the spell flame strike has as its area a cylinder, its effect usually ignores obstructions, but this GM would not let a flame strike spell ignore, for example, a wall of stone spell that'd been cast to form a dome above creatures in the flame strike's area!)

This ruling does lessen the danger of the natural-1-on-a-saving-throw-and-see-an-item-damaged rule, but this GM is comfortable with that, viewing that particular rule as a throwback to the hoary days of insult-to-injury Gotcha! DMing anyway.

That said, in my campaigns here's how the examples work.

• The spell shatter, when it's used—as described in its second paragraph—as an area spell

  destroys non-magical objects of crystal, glass, ceramic, or porcelain. All such unattended objects within a 5-foot radius of the point of origin are smashed into dozens of pieces by the spell. Objects weighing more than 1 pound per your level are not affected, but all other objects of the appropriate composition are shattered.

  However, according to the spell's second saving throw entry, a creature in the area that's attending objects that such a shatter could affect makes a Will save to negate the spell's effect. Yet all of a creature's attended items are affected if the creature either fails the Will saving throw or rolls a natural 1 on the Will saving throw, so, ultimately, it doesn't matter, the results of either being identical. (This GM would have an appropriate magic item possessing a higher Will saving throw bonus than the attending creature make its Will saving throw separately. Then this GM would chide that creature for have a weaker will than its magic items.)

• The aforementioned spell fireball says specifically that it damages objects. Thus the spell fireball damages unattended objects within its area, and a creature that rolls a natural 1 on its Relfex saving throw against the spell will find that one of its attended magic items has suffered fire damaged.
• The spells cone of cold and the aforementioned flame strike do not say they damage objects. Thus the spells cone of cold and flame strike leave their surroundings untouched, and a creature that rolls a natural 1 on its Reflex saving throw against either spell will find its attended magic items undamaged.
• The spell chaos hammer describes its damage as being dealt first to "lawful and neutral (not chaotic) creatures" then to "creatures who are neither lawful nor chaotic," yet the spell is silent on objects. Thus the spell chaos hammer—although its effect's described as a "multicolored explosion of leaping, ricocheting energy"—leaves its surroundings untouched, and a creature that rolls a natural 1 on its Will saving throw against the spell will find its attended magic items undamaged.
• The spell slay living requires the caster to "succeed on a melee touch attack to touch the target," and that target must be a living creature. The spell slay living doesn't affect an area (so its surroundings are (ahem) untouched), and it can't damage objects, so a creature's natural 1 on the spell's Fortitude saving throw doesn't slay one of its attended magic items.

I should note that the alternative gets messy. For example, not only will a warrior find his tower shield (that most portable of barriers—no matter how ill-advised) dissolving under assaults that would've previously left it unharmed (having, after all, only hardness 5 and hp 20), but also remember that areas are usually solids not planes, even though they are often represented as planes for convenient grid placement. That means casters must become extremely cautious or find their spells destroying the very structures on which they're fighting, and dragons must be wary lest their breath weapons collapse their own lairs! That is, the alternative would see every 5-ft. square of terrain in an area dealt damage, and that damage may destroy the very adventure site, not to mention, inadvertently, the party!

So that's this GM's standard for whether or not a spell affects objects, unattended or not and area spell or not. I'm not, like, utterly inflexible on this, though. For example, because a ray is like "using a ranged weapon," such a spell could be directed at anything (including objects or the darkness), and the spell'll affect objects appropriately (e.g. the spells scorching ray and polar ray as ranged energy attacks deal one-fourth or one-third damage to objects, but most objects will be unaffected by the spell ray of enfeeblement). However, a caster that wants, for example, a spell like cone of cold except that it also damages objects in the area like fireball (only, y'know, in a cone and with cold) would have to research and design that spell.