How fast time passes in Village Sim depends upon the game speed that you have set. You can keep track of how much time has passed by noting an individual villager's age as you play the game. On normal speed, the villagers will age 1 year for every two realtime hours that pass. Slow speed is 1/2 that rate, and fast speed is double that rate. So, on fast speed, a mom will nurse her baby for approximately 2 hours (although it's usually a little bit longer than that).
Most of the puzzles are dependent upon some combination of Village Tech, population, villager skills and other puzzles, so there isn't a single answer that will apply to all puzzles. Usually, if you get the message that you need more research it means either that you lack sufficient Village Technology in one or more areas, or you haven't completed the prerequisite puzzles (or both). The game doesn't care how many research points you have accumulated - it's the purchase of the technologies that enables the puzzles. Most puzzles can be worked on by any villager, but some require specific skills (most notably construction).
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