Solution:

811105 is the highest number that can be formed moving two matchsticks.

If your answer was 511108, you're almost right. All you have to do is look at that upside down. See the first picture and then the second.

Solution:

The Bangladeshi seaman is the thief. This is because the Japanese flag cannot be identified as upside down as it is the same both ways. Thus he is just trying to escape the situation.

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

They use the bricks and dirt from the tunnel to stand on it.

Solution:

All Digits [0-9] follow the following pattern: There is one occurrence of all digits in every 10 numbers Example. Digit-9 occurred one time between 10 and 19 in 9, between 20 and 29 in 29
However, for tens(91,92,93...99) and hundreds (900,901.... 999), the occurrence is much more. Since we have included 1000, Therefor 1 is the most occurred digit.
Note: Despite three '0s' in 1000, 0 is not most occurred digit as they don't have tens and hundreds like other digits.

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

The matchsticks that are marked with red are to be removed and the final figure will have just two squares. You can remove either pair from the possible four ways.

Solution:

1 2 3 4 5 6 and 7 8 6

Since summation of numbers 1-9(1 2 3 4 5 6 7 8 9) is 45 , so its impossible to divide into two equal parts.
Since we cant flip over 6 to make it 9 but we can flip 9 to make it 6 and hence the solution

Solution:

2003.

Explanation:
Its a series of prime numbes.

Solution:

Shikhar hit a sixer and then got retired hurt.
Suresh Raina came but he got run out after he and Kohli had crossed halfway.
On the next ball, Kohli scored a six and was not out at 100.

Solution:

Although it looks complicated, the answer is simple. The password to his computer is JIGSAW.
1st letter of Jug = J
2nd letter of Birthdays = I
3rd letter of Fights = G
4th letter of Cars =S
2nd letter of Laptops = A
1st letter of Watch = W