Can you find a number that lies one third of the distance between 1/3 and 2/3?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.

Complete the table series riddle by finding the number that can replace "??".

Find the hidden panda in the image below.

Can you count the number of squares in the given picture?

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

Rose, Lily and Jasmine decided to buy flowers for their moms on Mother's Day. One of them bought lilies, the other roses, and the third one jasmines.
'It's funny!' said the girl with roses, 'we bought roses, jasmines and lilies, but none of us bought the flowers matching her name'.
'You're right!', said Lily.
What kind of flowers did each of the girls buy?