What is both possible and impossible at the same time?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

No matter how little or how much you use me, you change me every month. What am I?

Different lights make me strange by changing me into different sizes. What am I?

There is a movie name hidden in the picture that is attached with this question. Can you find out which movie is it?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Solve the following series:
AZ, GT, MN, __, YB

Why is 6 afraid of 7?

A man walked into a pub and went straight towards the Barman. He asked for a dirty martini from the Barman. The Barman thought something and then pulled out a pistol from his drawer and aimed it directly at the man. Why did he do that?

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?