>>Puzzle 2.
>>
>>One person was lost in a forest. He knew, that there are two villages near the place, he was lost. In one honest people live, who always tell the truth. In the other, in opposite, knaves live, who always answer false. He met a person on the crossroad and asked him just one question, which helped him identify the correct road. What was the question, he asked?
>
>Here is the question
>
>"If you were from the other villiage, which way would you tell me is the right way home?"
>The truthful person, would have to pretend to be a liar, and point the wrong way.
>The liar would have to pretend to be a truthteller and point the right way, but because they lie, they would then tell them the opposite or wrong way.
>
>You would take the way that the person did not point. Correct?

Yes, though this is the most complicated solution.

I solved it similarly, e.g. "If I ask you, does this road lead to the honest village, what would you tell?" However, the simpler solution would be: "Do you live in this village?" (and show in either direction). I let you find the logic in all cases by yourself.

BTW, nobody solved the first puzzle so far. I've realized. that circle would not help, since the last one still don't know the color of its hat and you didn't tell the strategy. However, the circle is not allowed anyway, so try to solve the original puzzle. It's quite simple, I solved it in a train...