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:
First of all, pick a baseline damage: d6 for a low damage effect, d8 for medium damage, and d10 for high damage. If the damage can happen more than once, reduce the size of the die. So, for a continuous effect or a trap that goes off every round, the damage is d4, d6, or d8.
Now decide if the damage is leveled. The idea is the same as the one I discussed above for setting DCs. Tripping and falling into a campfire isn’t leveled. It’s just stupid. Stout, hardy heroes are more likely to shrug off that blunder. So that damage isn’t leveled. But if the fire trap is in Tyracticus’ Fortress, you can damn well bet he’s using magical super hellfire. It’s leveled as hell.
If the damage is leveled, roll half as many dice as the PC has levels, with a minimum of 1. At first level, if you want to, you can reduce the die size. Up to you. I find it doesn’t make much difference and it’s only for one level. If the damage isn’t leveled, roll 2 dice.
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.
There are no rules that cover this specifically, but you can use the movement rules as guidelines.
Characters have speed and movement. If you have a speed of 30 in your Druid, and move 30ft, then you have no more movement left. If you shapeshift into something with a speed of 50ft, you now have 20ft of movement left.
Do the same with breath. You could hold your breath for 5 minutes as a druid and spent those. Shapeshift into an octopus, and you can now hold for another 25m. Shapeshift into something that couldn't breathe above water ever, and you'd start suffocating regardless of how long you had held your breath.
TL;DR: option 3.
Best Answer
Check out the Suffocating rules
The rules on suffocating can be found in chapter 8 of the PHB, or just in the basic rules such as on D&DBeyond:
In your case, the DM can make a ruling
However, the above does not cover your specific situation. If you take damage whilst holding your breath, the rules are silent on whether the creature damaged should suffer any penalty with regards to holding their breath.
One of D&D 5e's mantras is "rulings, not rules", and this is one such case for that. As a DM (I'm assuming you're the DM in this scenario?), you could come up with a ruling for this situation; I would suggest something like a CON save with some penalty for failing, such as losing 30 seconds worth of holding your breath, or even just "you aren't holding your breath anymore". But such a ruling at that point would be something the DM would come up with on-the-fly (although, once such a ruling has been made, it's best to be consistent with it henceforth in the interests of fairness).