Solution:

If You can read this you are awesome.

Solution:

White should move the rook from
A1 to D1 and hence complete the castling move.

Solution:

Solution can be verified from the picture below.

Solution:

Karate Kid (car + at + tea + kid)

Solution:

Slumdog Millionare = Slum + Dog + Million + air

Solution:

The three errors are as follows:
a) fynd is spelled wrong. The correct spelling is 'find'.
b) that is not appropriate to use here. It should be 'this'.
c) There are only two errors in the question and that is the third error because the questions asks us to find three.

Solution:

The attached picture shows you how you can do it. If you were able to deduce any other way, feel free to comment.

Solution:

2 cakes

At each toll bridge you are required to give half of your cakes, and you receive one back. Which leaves you with 2 cakes after every bridge.

Solution:

The competition was held on 11 November 2013. The logic is simple. In America, the dates are mentioned as Month/Day/Year and in Britain, dates are written as Day/Month/Year. But on 11 November 2013, the date and month will be the same. And thus both will write in the same manner i.e. 11/11/2013. If it would have been any other date, the evaluators would have been able to identify it.

Solution:

Either your read from start or from ends, it will be same

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)