What does does this rebus picture means ?

What's the only room from which no one can enter or leave

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?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

What number comes next in this sequence:
7 8 5 5 3 4 4 _

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

A little girl goes to the store and buys one dozen eggs. As she is going home, all but three break. How many eggs are left unbroken?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

Using eight eights and addition only, can you make 1000?