What does this rebus puzzle means ?

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

Baseball bat and ball cost $100. If the bat cost $99 more than the ball, what is the cost of each?

Can you count the number of squares in the given picture?

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?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

In a particular village, only two barbershops exist.

The first shop has a handsome barber with a neat haircut who is handsomely dressed in clean clothes and is extremely humble with his body language. The place is clean and looks hygienic.

In the second shop, you can find a barber with shabby clothing. His hairs are weirdly cut and his clothes still have the stains from last night's dinner. The place is not clean as well and reeks a bit.

You visit the village for the first time and decide to get your haircut. Which barbershop will you like to go for that and why?

Can you find the company name in the pictogram below?

There are two candles. Both will only burn exactly for an hour. How will you use these two candles to measure forty-five minutes?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?