What can I use firewood for? Is the supply unlimited?
I found a wood axe and a chopping block near to each other in a camp somewhere and so became aware that I could use the axe with the chopping block to (very slowly) produce firewood.
Does firewood have any purpose other than just being low-value merchant fodder?
Can I set up camp fires, maybe, or something else?
Also, does a chopping block ever run out like ore seems do?
(I got bored quickly so didn't test more than a couple of chops)
In most of the locations where you can chop firewood, there will be an NPC nearby who will buy any firewood you chop for 5G a piece. Early in the game, it's a nice way to raise a few coins while running AFK to grab a drink or while typing up a question or answer here at Gaming.SE.
Firewood is also used to improve a few low level weapons, notably the Long Bow, at a grindstone.
And yes, the supply is unlimited. The truly dedicated could chop enough wood to buy and furnish a house.
You can use the firewood to create arrows at a blacksmith's forge if you have the Dawnguard DLC.
Ebony arrows require a Smithing level of 80 and the Ebony perk to create.
1 x Ebony Ingot
1 x Firewood
Daedric arrows require a Smithing level of 90 and the Ebony perk to create.
1x Firewood
1x Ebony Ingot
1x Daedra Heart
Dragonbone arrows require a Smithing level of 100 and the Dragon Armor perk to create.
1 x Dragon Bone
1 x Firewood
Firewood just seems to be low-value merchant fodder. There are a few more of these things, for example you can go to a saw mill and load logs/ cut them, you can pick crops for farmers and get paid for it. Doesn't have much a purpose other than to add a bit of average joe jobs to the game.
It is also probably put in the game by Bethesda as a modders resource. They probably think that when the construction set comes out, someone will make it so you can light a fire or put them on extinguished fires at camps. Mostly, it is just used for making some easy gold.
Go to Whiterun and then in front of The Bannered Mane is a wood cutter block. Use it then go inside and sell your firewood. Easy profit :D