Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

Can you spot what's wrong with the following sentence?

PETER WAS ANGRY AT
HIMSELF BECAUSE HE
ACCIDENTALLY LEFT THE
THE KEYS TO HIS CAR
AT HIS FRIEND'S HOUSE.

What number comes next in the series?

5 15 5 18 5 24 14 20 _

how come the second man dies?

You can find some missing letters in the picture. By placing two particular letters in the spaces, you can form a nine lettered word beginning from one of the corners and going clockwise direction to the middle. Can you find out the letters and the word?

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

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

The dirtier I get, the whiter I look. Who am I?

Why do people go to bed?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?