Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

I look at you, you look at me I raise my right, you raise your left. What am I?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

Below toothpicks/matchsticks indicate the group of fishes moving from west to east direction. Can you make them move from east to west by just moving three toothpicks/matchsticks?

Which English verb becomes past tense just by rearranging the letters?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

Outside a tattoo artist's shop, there was a signboard which read 'I make tattoos on only them who do not tattoo themselves'.

Reading it what do you think, does the tattoo artist tattoo himself?

Can you find out who is the kidnapper in below Picture and why, Explain ?

The following four words might seem abrupt to you. But you can make them meaningful by just adding vowels.
RDSH
GGPLNT
TMT
NN

Hint: All of them are vegetables.

John has eleven friends. He has a bowl containing eleven apples. Now He wants to divide the eleven apples among his friends, in such a way that an apple should remain in his bowl.
How can He do it?