Solution:

The Hundred Years war lasted 116 years from 1337 to 1453.

Solution:

The receptionist was pretty clever she played with the mute button of the phone while talking with her mother. She muted everything except the word emergency, call and help. So while talking, she sounded like 'Emergency… Call… Help' to her mother and thus she called the police.

Solution:

I caught zero fishes.

Explanation:
I in Roman Numeric system denotes 1. Taking off 1 from 10 makes it 0.
Taking off tail of 9 makes it 0.
Chopping off the head of 6 makes it 0.
Dividing 8 in half makes it 0 from either side.
Thus, in total, I caught 0 fishes

Solution:

The pills can run for an hour.

Explanation:
If you had ninety minutes in mind, then you are wrong. You took the first pill at the zero minute. Then you took the second pill after 30 minutes and the third pill after 30 + 30 i.e. 60 minutes or an hour.

Solution:

The young lady was presented with a bill which belonged to the elderly woman. She had asked the waiter to collect the bill from her daughter.

Solution:

To do this, he must be pushing the cork inside the bottle and then taking out the coin.

Solution:

None of the rungs will go underwater.
This is because as the tide is rising, the ship is also rising and with it the rope ladder is also rising. Thus none of the rungs will go underwater ever and it is not related with the distance between the rungs.

Solution:

8 is the required number.

Here, by dividing in half, we will actually chop off the digit from the middle. Then you will be left with two zeroes.

Solution:

It was easy as it was daytime. They did not need headlights or the light on the number plate.

Solution:

Diwali was celebrated as a mark of Lord Krishna win over the Narakasuna by killing him. Now Krishnavathaar comes after Raamavathaar in the Dasavataar. Therefore, Lord Rama could not have celebrated Diwali.