Solution:

J = 1
O = 9
I = 6
N = 8
T = 3
(1+9+6+8+3)*(1+9+6+8+3)*(1+9+6+8+3) = 19683.

Solution:

The women is a of short stature. She can't reach the upper elevator buttons, but can push is with his umbrella.

Solution:

The Password.

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

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

It can be solve as shown below.

Solution:

It can be solved as below.

Solution:

192 021

If you look at it as two-digit numbers you'll see:10 11 12 13 14 15 16 17 18 19 20 21

Solution:

3 1 2 2 1 1
1 3 1 1 2 2 2 1

Read Line as one 1 => 1
Read Line 2 as two one => 2 1
Read Line 3 as one two and one one => 1 2 1 1
and so on.

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:

The attached picture gives away the solution. If you can find another solution, do send us yours.

Solution:

Can be found on the pic below.