If they have nothing to do, they go into a city and sleep forever. If you press the button again and there's something to do, they'll go to work. What probably happened is that lumber mills weren't available at the time and at this point decided to stop working completely.
Do not have them be able to replace old improvements. Chances are they will ruin everything as they waste time trying to replace improvements and screw everything up. Furthermore, you should be manually improving tiles for at least your main cities and overwriting those is bad. If you end up with a bunch of workshops in your floodplain city, or cottages in a grasshill dominated city, you will regret it.
At the very least, you absolutely want to manually improve your special tiles, in particular food (any food resource) and commerce ones (gold, gems) asap. Don't compromise on this. So even if say, you don't know what to build on a particular tile, you want to get those done first.
Until you've secured at least a decent position, you shouldn't automate workers. If you find various bits tedious, later on, you may delegate a worker or two to "Build trade network", which saves you the tedious task of having to road everything. But even in those cases they are inefficient. They will road to a resource first, and then improve the resource, which is terrible because it takes forever for you to be able to use it-- at least improve all your special tiles first. But fortunately, roading every tile is the lowest priority.
As a side note, automated workers also are suicidal and seem to run straight into enemies. Another thing you don't want to happen early game.
Now obviously, if you conquered your continent, have 20 cities, have nukes when they have rifles, and you don't want to bother microing captured cities that are half improved by AI, then sure, just win the game and let the workers do whatever. I actually do this sooner, because I hate microing end and rather play more quick games (1-2 hours) since I have divided my game time between a couple of games*, but this is not something I would recommend to people as that often means I am slumming down in difficulies.
Oh. and chop your forests. For whatever reason you have for keeping the forest, there's about 10 to chop it.
(Well, that was the plan. Guild Wars 2 is my main game. But since I bought Civ 5 and 6 I decided to spend some casual time between 4-6 when I have downtime for my main game. What ended up happening is 90% of my Civ time goes to IV.... figures. It helps that IV runs on crappy laptops when I am not home.)