Outside of a single specific POI (the Dump N' Lung mine) there is no coal generated in the desert. It is replaced in the world gen for that biome by oil shale (which does not spawn outside of POIs out side of the desert).
Yes. Last I knew it was in the southern ghost town. I haven't been back down there in A19 so it may have been replaced.
The devs made that decision, so unless they've stated their reasons somewhere we don't know for certain. Best I can figure is to give a reason to leave the desert or enter the desert from time to time. 7d2d is not currently designed around single biome play throughs (probably will never be), which is why it takes a 3rd party program to get single biome maps to generate.
We are on day 150 and have did 99.9% of the play through just in the forest. The only reason we've had to leave is to travel less than 50 blocks in to the desert to get sand and oil shale. With being able to get sand from stone and gas from breaking down vehicles I would say it would be easy enough just to live in the forest. I would love for other reasons to go in to the different biomes. There is currently no reason to go to the snow, wasteland, or burnt areas of the map and that sucks.
In the desert all coal is replaced with oil shale as part of world gen so the only way to get coal is to find it at POIs or buy it. Which you can find it at quite a few POIs like the a for mentioned coal mine, factories, and the metal works has some but even better is chopping up burnt homes as you get wood and coal from burnt wood blocks.
