1. I don't think so except for the entertainment value and/or to gather all villagers in one area.

2. Don't know. I believe so since the Chief just points out rare collectibles in general without specifically pointing out missing ones (which would be better).

3. According to what I have read on other posts and my own experience, no, only missing tablet pieces pop up.

4. There are other threads that would be helpful to you. If you leave the game running with plenty of food for a couple days or so, then when you come back you might have over 90+ year olds.
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Read my story: The Forbidden Cave