(I have listed possible spoilers in white as the topic title doesn't include the word 'spoilers', if you want to look just Highlight!)
Ok, the first three numbered ones are just cute things they do! They can get annoying if you're trying to make them work, but you can just stop them doing any of them and put them back to work.
The kids skills improve whether you tick a box or not, they gain one bar of skill each time when you see a sparkle above their head!
Adults at lectures, I don't Think they gain any skills, again it's just cute to see them all together in the ampitheatre. But I've never checked to see if they gain skill so they may do.
Dancing I think once they have done the weather dance that's it, they can do it again by putting them on the fire. The rain does have a function though: It makes the lift work. If you put a villager on it just before it rains, a fruit will drop down which you can plant to make a fruit tree.
The chief points out rare collectibles if you have level three leadership, but not necessarily one you don't have. Put the chief up on the top of the path next to the secret door and he'll have a little think then point one out. Just take a spin round your village and you'll find one.
I don't think the chief points out mushrooms though, one might appear when you put the chief up on the path but it'd just be a coincidence.
Hope these help!