Solution:

She was playing baseball.

Solution:

4 6 5 3 (from magician perspective)
3 5 6 4 (viewer perspective)

Detail:

From user perspective:
3 5 6 4 => 5 6 4 3 => 6 5 4 3

For magician perspective
3 4 5 6 (ascending order as)

Solution:

They used the planks in the manner that is shown in the figure.

Solution:

Here is a way to do it. We dont know if it can be done using some other arrangement or not. If you know, do send us.

4 | 3 | 8
9 | 5 | 1
2 | 7 | 6

Solution:

Remove the same 2 matchsticks from each figure and move figure towards left 45 degrees, It forms the letters V W X Y.

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

The Password.

Explanation:
Clues 2 and 5 are correct and rest are lies.

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:

The husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

We now have a square of 3x3 size, 2 squares of 2x2 size and 5 squares of 1x1 size.