What does an Island and the letter T have in common?

If you had an infinite supply of water and 5-quart and 3-quart pails, how would you measure exactly 4 quarts? What is the least number of steps you need?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

I have eight fingers and two thumbs but I do not live. What Am I?

When can we add 2 to 11 and get 1 as the correct answer?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

Fate has decided that you will only be pleased to meet me when you need me

Maybe that is why, when I am working, I start working

However annoying I may be to the regulars, the little ones are always inspired

I will always be waiting if you try to reach me

How many of you can guess my name, let me see

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?