How to stop people using coal as fuel in their houses

Well like you said, Farmer is 1 of them. They will only do their farming from early spring to early autumn. Besides that, traders only do their job when a merchant is present. I personally keep the farmers on their job at all times. And take the traders off their job once there is no merchant in sight.

Finding the right balance for your farmers/traders in the "off-season" is really dependent on where you need them the most. If you need food, give them a gatherer job. If you need buildings send them off building.

Managing population fluctuations, both local and city-wide, is one of the biggest challenges of Banished. But with the right technique, it isn't one which can't be overcome.

When you need some household to migrate to another location, build a new house for them in the new location and just before the new house is finished, order their old house to get removed. They will then become homeless and migrate to the new house the moment it is finished.

Single households are in fact quite handy in this regard, because they give you a higher flexibility (you can move a single worker and don't have to move two at the same time). The downside is, of course, that more houses require more resources to build and more fuel to keep warm.

As a result of population fluctuations you will soon notice that workers who used to live close to their jobs will switch jobs and have suddenly a new job which is far more remote. To solve this issue you should regularly (every couple years) unassign all jobs by making everyone laborers and then reassign the desired number of workers to each occupation, starting with those where you consider proximity most critical. When you add a worker to an occupation, the laborer closest to an open job of that occupation will be converted, so by reassigning regularly you can re-optimize who does which job.