[RPG] How much damage does generic, non-magical fire do per round

1. RAW interpretation:

   Torches would deal 1d4 unlit as an improvised weapon and only 1 lit as per torch description, specific overrules general.

   A reason for this by RAW could be it's burning, twigs and sticks that are alight are brittle and fall apart at the softest touch.

2. Rules as Intended/Logic

   Torches are usually a bunch of reeds, sticks, cloth and other flammable substances attached to a piece of wood, of which the strength there of may vary (DM's decision whether it is a solid piece of oak or a simple flex of more solid branches). They can be fairly flexible but brittle too and therefore not really appropriate to be used as an improvised weapon. Think hitting someone with the equivalent of a pool noodle, that's not going to do 1d4 damage.

   Just because rules allow for many things to be used as an improvised weapon does not mean that anything and everything can/should be. I stab him with my sewing needle, it's an improvised weapon, I deal 1d4 damage. Common Sense Rules.

   Torches cannot practically be used as an improvised weapon, they would most likely break apart after one hit. So would deal no damage as a weapon unless lit when it deals 1 fire damage.

3. DM Allows Torch as Improvised

   If your DM is going to rule that they can be used as an improvised weapon then they would deal 1d4 bludgeoning and if lit 1d4 bludgeoning + 1 fire damage.

Setting DCs

First of all, if there is no time pressure and no consequence of failure and the action is possible then they should just succeed. This applies for everything, not just lighting fires.

However, in the specific instance of lighting fires: if they have a tinderbox and something to burn and its not pouring with rain then they can start a fire, be it a torch, a campfire or a cigarette. Setting fire to something else under the same circumstances when you already have a fire should be quicker and (possibly) easier.

Its only when there is time pressure, or there are consequences of failure or there is some question mark over possibility that you need to set a DC.

When setting a DC you should look and see if the rules have a section like "How to set the World on Fire" - they don't. Pity.

So you have to make them up. Its always a good idea to look at other rules to see if you can nick their DCs. Offhand nothing springs to mind so we are going to have to wing it.

So what is the action the PCs want to accomplish? Well, its unclear from your question if they are trying to kindle a fire from scratch or use an existing fire (like a torch) to light something else. Let's see if we can deal with both.

Lighting fires from scratch

Hunting through my PHB my eye lights on this (p.153):

Tinderbox. This small container holds flint, fire steel, and tinder (usually dry cloth soaked in light oil) used to kindle a fire. Using it to light a torch—or anything else with abundant, exposed fuel—takes an action. Lighting any other fire takes 1 minute.

So here is an item that gives us our staring point. So if we have something highly combustible it takes 1 action to light, if not it takes 1 minute. Now, 1 minute is like forever in combat (10 rounds) - the longest combat I have ever seen in D&D 5e was over in 5-6 rounds, so if you are planning to do this in combat then whatever you are lighting had better be as combustible as hell.

I also noted (p.152):

Oil ... You can also pour a flask of oil on the ground to cover a 5-foot-square area, provided that the surface is level. If lit, the oil burns for 2 rounds and deals 5 fire damage to any creature that enters the area or ends its turn in the area.

So 1 action to pour the oil over the thing you want to burn and 1 action to use a tinderbox to set it on fire, or if you have something already burning you can light it for free (I would rule).

Now in neither case is a DC called for. Provided you have the tinderbox, you can light a fire given something to burn and enough time (1 action or 1 minute). Good, lighting fires is easy.

Setting something on fire

Remember the rules (this is basically all of the rules: everything else is just nuance :-)) (p.6):

1. The DM describes the environment
2. The players describe what they want to do.
3. The DM narrates the results of the adventurers’ actions.

The DC swings on what you decide is in the environment:

• What is the house made of: did the little piggies make it out of straw, sticks or bricks?

• What type of tree: a willow, a pine, or a eucalypt?

• Is it summer or winter or autumn?

• Has it been raining?

• Is there 3 feet of snow on the ground?

• etc.

Thinking about all those things you do what experienced DMs do: lick your finger stick it in the air and make something up. Of course you can always use the Table on p.238 of the DMG:

Task      DC  Task              DC
Very easy  5  Hard              20
Easy      10  Very hard         25
Moderate  15  Nearly impossible 30

Even better, you can use this advice on the same page:

If the only DCs you ever use are 10, 15, and 20, your game will run just fine.

Which means that you only need to decide if the thing is easy to light, hard to light or somewhere in the middle.

Depending on what the players tell you when "The players describe what they want to do" they can earn themselves advantage ("I throw oil all over the thatched roof and shove my torch inside") or disadvantage ("I hold my torch against the timber wall until it lights") or neither ("I set fire to the house").

We already know how long it takes - if it is something easy to light (DC10-) it takes 1 action, if its harder than that it takes 1 minute.

Effects

The effect of a fire in terms of damage, growth and spread is a whole question on its own I think.