Solution:

She simply asked everyone to raise hands on hearing the question. The only condition was that the ones who knew the correct answer will raise right hand and other will raise left hand facilitating her in acknowledging the ones to pick for answering.

Solution:

I am a battery.

Solution:

Its day time

Solution:

Sucide

Solution:

2, 3, 10 and 10
To maintain the difference of eight and keeping in mind the third and fourth hint, the first and third cards can be 2 and 10 or 10 and 2. But keeping in mind the first hint, we know that the first card is 2 and the third is 10. Similarly, if we see the fifth hint, the difference between the second and fourth card should be 7. Thus we know that the second card is 3 and the fourth card is 10.

Solution:

China

Solution:

The answer is 0.
As
6 / 7 = 42 but the answer is written as 2
3 / 9 = 27 but the answer is written as 7
8 / 2 = 16 but the answer is written as 6
If we look at the answers, the second digit has been used in the problem.
Now, as
4 / 5 = 20 and the second digit is 0, the answer is 0.

Solution:

I live in a Chess Board.

Solution:

A River

Solution:

The plane was not flying :p