Solution:

It is a baby's face as you can see in the answer picture.

Solution:

The person on 73rd number will survive.

Explanation:
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.

Solution:

Upon reaching each room, he found out that the window facing the dead body was closed. He had to open the window himself. This tells that there was somebody else with him who closed the window. If he would have committed suicide, at least one window would have been open.

Solution:

In the picture you can find the green matchsticks. We have moved them from the bottom and placed them in the middle. It was a bit tricky but now you have your desired result.

Solution:

23rd day

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 + 22 + 23 = 276

Thus our anniversary falls on the 23rd day of the month.

You can apply other formulas to shorten the process but that is the simplest way to do it.

Solution:

128

Explanation:
If we start from the small squares and the move up the scale, we can identify them without a problem.
1x1 squares = 62
2x2 squares = 41
3x3 squares = 18
4x4 squares = 6
5x5 squares = 1

Now, totaling them, we get:
62 + 41 + 18 + 6 + 1 = 128 squares.

Solution:

Yes there is a way considering if you can find a magnifying glass. Using the bright sunrays, you can then burn away the string allowing the ring to fall down on the bottom of the bottle.

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 package comprises of the parachute which is tied to her back while she is diving free in the air. If she doesn't open that, she will hit the land and will die.

Solution:

Watch the video for more detail.