Solution:

Fire

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:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.

Thus both will be happy in such manner.

Solution:

Read the question carefully again. New Year do falls after Christmas but that happens if two different years. The question is put up against the year 2050 and thus there will be 51 weeks and 2 days in between them as New Year will appear on 1 January 2050 and Christmas will happen on 25 December 2050.

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:

To do it, the marbles must be arranged as the vertices of an octahedron. If you are unsure, check the image below.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

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

Solution:

On Your lap.

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