Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

I have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

What does the below rebus puzzle mean?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

In two decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

I cannot talk, but I always reply when spoken to. What am I?

1 + 9 + 8 = ?
considering, 28 + 8 + 92 = 10