There is only one place that your villagers need to clean, and that's the beach.

The villagers don't always fix huts - it's an activity that they perform when they determine it's necessary. If you're only checking on your villagers occasionally, you may not see anyone fixing a hut. Your progress in the game is not affected by how often they do that.

There are two different types of improvement in Village Sim: individual villager skills as indicated on the details screens, and overall Village Technology, as indicated on the Village Tech screen. Inidividual villagers improve their skill by working at tasks around the village: Farming, Research, Breeding, Healing, and Construction. The more skilled a villager is in a particular area, the more effective they will be when they work at it. For example, a Master Scientist will produce more research points each time they work at the research table than, say, a Trainee Scientist will produce. A villager can continue to perform a given task after they have maxed out that skill, but they will no longer improve in that area. In the Village Tech screen, you use the research points produced by your scientists to "purchase" higher levels of technology, which will enable you to achieve the goals of the game (such as solving puzzles).