The short answer is that your Order of Operations is correct for both the attack and the Fireball. The rules use the phrasing "takes damage" consistently throughout.
The example given in the Damage Resistance and Vulnerability section (page 197 of the PHB), answers a lot of your questions.
For example, a creature has
resistance to bludgeoning damage and is hit by an attack
that deals 25 bludgeoning damage. The creature is also
within a magical aura that reduces all damage by 5. The
25 damage is first reduced by 5 and then halved, so the
creature takes 10 damage.
So, the raw damage is phrased as "an attack
that deals 25 bludgeoning damage". Then all the calculations are done, then the final result is phrased "the
creature takes 10 damage". Warding Bond says that
each time it takes damage, you take the same amount of damage.
Therefore, the Cleric will take the actual amount of damage that was applied to the Paladin's hit points after all the resistances and saves were calculated.
Fireball won't change the order of operations, since the Dexterity save determines how much damage the Paladin takes. For proof, we can go to Fireball itself:
A target takes 8d6 fire
damage on a failed save, or half as much damage on a
successful one.
Or, to put it differently, a target takes half as much damage on a successful save.
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.
Best Answer
Specifically, the effects of Gunpowder exploding is covered in DMG 267, under Explosives. And Oil is covered in PHB 152, but only for a flask.
Broadly, rules for Improvising Damage is in DMG 249, where it lists various examples and the amount of damage, by increments of d10s.
If you don't like memorizing all those bits, or are still having trouble improvising the damage, you can read: The Angry GM’s Marvelous Mechanical Miscellany for Ad Hoc Adjudication and Improvisational Invention (WARNING! TheAngryGM link, contains swearing and beating people with their copies of the DMG). It gives clear guidelines on how to improvise setting the DC, and how much damage an effect should do. I'll quote some of it here, in case the link goes dead:
I've personally tried this method, and have found that it is not as punishing as I like, so I stepped up the damage die in the baseline damage to d8, d10, and d12.