what does the below math rebus puzzle mean?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

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?

Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.

What word is identified by the below rebus?

Your Your Your Your Your
Your Your Your Your Your

I’m tall when I’m young, and I’m short when I’m old. What am I?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

When we see 2 but call 10?