Don't accent the rules — describe what happens in the world
Decide what you’re trying to accomplish first, then consult the rules to help you do it. As a DM, you help guide the narrative and bring the world of the adventure to life. From this perspective, the rules are not directions, but a tool:
The rules serve you, not vice versa. (DMG page 235)
When you make a ruling, in order to prevent arguing, ensure you provide a plausible in-world explanation for players (e.g. "you can't put this trinket in your mouth, because you have no time", not "because the rules say so").
Considering the provided example — casting the Darkness spell on an item and hiding this item in a mouth is actually a clever idea. But your player's intent wasn't to invent a smart tactical move, but to "trick" the game world by abusing the turns mechanic.
But you can't trick the world. Unlike a computer game, the game world in D&D is not the mechanics, that's why DM is needed in the first place. Distinguish between what happens in world (what character see) and what mechanics do you, the DM, use for resolving the situation. Explain, why sitting in complete darkness is a bad idea:
— I could cast darkness on the lip piercings.
— It will effectively render you blind in the middle of the combat, are you sure you're doing it?
— But I can cover the darkness when my turn starts, can't I?
— Not exactly. We (players) use 6-second round mechanics to organize the combat pace, but for your characters there are no "turns". They are just fighting the bad guy and all act simultaneously. You can dismiss the darkness when you hear something, I will use the Ready action to resolve it. Do you do this?
More info - How does time pass in combat?
Low stats do not mean low participation.
Just because a character does not have high numbers in a particular stat does not mean they cannot participate in any particular encounter. As someone who's played a 5e bard, the fact that you and your player think they're worthless in combat is baffling to me. Why are they only shooting a crossbow when they're arguably one of the most versatile casters in the game?
Likewise, just because your barbarian has low CHA and INT doesn't mean they can't interact with NPCs. I've seen (and played) characters who were obnoxious, dumb oafs that nevertheless manage to engage in entertaining social interactions. A low CHA does not mean that you're shy--it just means you might be bad at lying, for example.
Ultimately, a character is more than their character sheet--they (ideally) have personalities, motivations, and preferences beyond their specific stats. In fact, it's sometimes more fun to have characters that are really bad at things they like to do, like a talkative CHA 6 character.
Explain this to your players.
Your players need to understand that they do not need to be slotted into specific gameplay niches. Most social interactions, for instance, don't actually require rolling checks--your barbarian can still talk to bartenders and ask for information. Likewise, almost every class has something useful to do in combat! Because you say that your players are willing to play both combat and RP, you should emphasize to your players that their gameplay is not fully determined by their stats. Instead of asking themselves, "Who has the best stats to engage in this interaction?" they should be asking, "What would my character be doing in this situation?"
This problem is also partially due to the players' self-imposed limitations. For example, if the bard doesn't have damaging spells, then they're throwing that part of their class away. How would you react to a fighter that refused to use a weapon? Hence, you need your players to accept that they should build characters that are useful in your campaign. When I played a bard, the only damaging spells I really used were Vicious Mockery, Dissonant Whispers, and Fireball--the rest were utility spells, and it worked well.
Create situations where character abilities are relevant.
Once you have buy-in from your players, you should build scenarios and encounters where players' abilities are relevant.
For social encounters, you can build in checks that are not CHA based. PHB 175 describes this variant:
Normally, your proficiency in a skill applies only to a specific kind of ability check... In some situations, though, your proficiency might reasonably apply to a different kind of check.
Therefore, your barbarian might be able to roll a Strength(intimidation) check to intimidate an NPC with a feat of strength, or a Constitution(performance) check to win a drinking game.
On the combat side, you can introduce intelligent enemies that will negotiate with the PCs during a combat. I've played and run a number of encounters that were half combat and half conversation--the skill monkey could play tricks that cause goblins to run away in fear, for example.
You'll have to be careful not to overuse these "crossover" tricks, lest you devalue the other side, but they're a useful tool to allow talkers to participate in combat and combatants to participate in talking.
Best Answer
There are no existing first party rules of this sort. Rules about fire in D&D are limited to fairly small fire spells and/or setting an opponent on fire at most. Related: How does fire work in D&D?
It's possible someone's published some third party rules in a splatbook somewhere, but they would likely be more oriented towards someone else set the fire and the PCs are trying to escape/stop it.
So what you'll need to do is take both a) your knowledge of reality and b) an appreciation for what will be fun and challenging in a game and come up with some rules yourself. There's not a "right answer" here. Don't put more detail into it than you really need to - you can make it as simple as a DC check of some sort (Int?) to see how well you get the fire going (<10 - someone sees you trying to start it, 10-15 the fire's seen as soon as it's started and it only affects the one building, 15-20 it really catches and burns down the building and adjacent buildings...). Once it's all done if the question is "did building X get burned down" say "20% chance it's still standing. yes."
You can make more of a minigame out of it if you want - lay out a map and there's a X% chance a round of adjacent buildings catching but local people fighting the fire make a DC Y check to put out a house, etc - but consider where there's any value to that additional work.
Needless to say things like this are always harder than they sound, and especially even if it works culprits are often seen or found out, and you have every right to sic a bunch of trouble on the PC from a) the law/ruler, b) everyone whose stuff was damaged or relations killed. In an at-all-realistic campaign, this is the point of no return, because after this the campaign becomes about the "Burning of Kislev" or whatever.