Solution:

Can be found on the pic below.

Solution:

It can be done as shown in the picture below.

Solution:

It can be done in image below.

Solution:

Yellow switch

The trick to solve this problem is to start from the bulb.

Solution:

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

Solution:

Solution can be verified from the picture below.

Solution:

As shown below, we can make equation as 6 = 6 = 6.

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:

We just added four matchsticks as shown in below picture.

Solution:

Solution is shown below,