Solution:

I am a compass.

Because I am a compass and I help people navigate all around the world.

Solution:

199 - 99

Solution:

You can ask this question to any one person, "if I ask the man who is next you: which is the correct way and the road to the village, what would the person next to you answer?"
If you happened to ask this question to the liar, he will show you the wrong way.
And if you happened to ask this question to the one who says truth, he will also show you the wrong way.
Once you are done with this, take the other way. This will lead you to the village

Solution:

A cigar stuck in the wall

Solution:

The Bangladeshi seaman is the thief. This is because the Japanese flag cannot be identified as upside down as it is the same both ways. Thus he is just trying to escape the situation.

Solution:

Daughter.

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

Hhe hung herself using big Ice slabs , which are now now melted and hence puddle of water.

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.