You need to fix up the house in the first town to get charcoal. Once you've finished doing that, you can make charcoal by interacting with the oven there.
As Search can be one's friend. Charcoal is made, the Pine Charcoal is made in the second city by the dude that makes steel, just to place here again. It is asked often enough.
On a differetn note:
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it basically states ver 0.52 of Forest of Abyss 3 will be the last before the full realise, and that realise is planned to be in December. (translated thx to "ImTranslator")
