What Deficiency does the below rebus represent?

VIT_MIN

I am first found in caves, now prolific online; I am a depiction, a drawing, a symbol, or sign. I will convey whichever mood you could wish; or for that matter, a fist, flask, or fish. What am I?

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

A famous swimmer can swim downstream in a lake in exactly 40 minutes with the lake current.
He can swim upstream in that lake in exactly 60 minutes against the lake current.
The length of the lake is 2 km.

How long he can cover the distance of one side at a still lake with no current?

If Rajina's daughter is my daughter's mom, who am I to Rajina?

If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

What number comes next in the series?

5 15 5 18 5 24 14 20 _

A certain street contains 100 buildings. They are numbered from 1 to 100. How many 9's are used in these numbers?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

What is the longest word in the dictionary?