Solve below rebus puzzle?

It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

Begin with a word, five letters to my name,
Remove the first and last but I am the same
Take out my middle and still, I remain.
What word am I?

Can you find the thief by just looking at the picture below?

Can you make numbers like 24, using numbers 3,3,7 & 7 with any arithmetic operator?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

What goes up but never comes down?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?

Quickly Solve this riddle

7 - 4 + 3 * 0 + 1 = ?

To tease, King Akbar told his most clever advisor Birbal to give his daughter one thing that she can eat when hungry, drink if she feels thirsty and can burn if she feels cold. King Akbar was shocked when Birbal gave Akbar's daughter one such thing that satisfies all of the above.

What did Birbal give to Akbar's daughter?