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?

Here is a conversation between a couple who both are software professionals.

Husband: Hey! What is your date of birth?
Wife Replied Angrily: It is 591062400
Husband after doing some calculations replied, "Got It".

What is the DOB of the wife?

What do you think with the below Picture ?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

A boy was at a carnival and went to a booth where a man said to the boy, "If I write your exact weight on this piece of paper then you have to give me $50, but if I cannot, I will pay you $50." The boy looked around and saw no scale so he agrees, thinking no matter what the carny writes he'll just say he weighs more or less. In the end the boy ended up paying the man $50. How did the man win the bet?

For this puzzle, you might have to find logic in something illogical. But hey, it's fun and a healthy little break from your strenuous puzzle-solving sessions.

Can you decipher the meaning in the following cluster of letters?

ITIT,NCENTCENT

I always drive my customer away.

Who am I?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

Solve the puzzle by telling what does below picture means.

Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E