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

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

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

What numbers should go on the bottom line?
3 6 9 15
8 2 10 12
11 8 19 27
19 10 29 39
? ? ? ?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

Can you solve below mathematical equation?

2^1234 - 2^1233

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

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

What can you hold in your right hand, but never in your left hand?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?