What does this below rebus puzzle mean?

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?

When I go in I might cause pain. I cause you to spit and ask you not to swallow. I can fill your hole. What am I?

I have four wings but can't fly.
I express no emotions.
I am found on the exact spot every time you look.
I keep toiling away with a little sound.

Do you know what am I?

Eight of us go fourth, not back, to protect our king from an attack. What are we?

Can you count the number of matches in the picture below ?

What is the last thing you take off before bed?

An inspection by the superintendent of St. Joseph School was scheduled on the next day. The class teacher Jenifer knew that he would be asking questions from her class and she would have to choose a pupil to answer. To offer a perfect impression over him, the teacher explained certain instructions to the students to maximise the chances of getting correct answer every time.

What did she say to the students?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

Rearrange the letters in "new door" to make one word.