Solution:

The letter 'n'.

wiNdow - widow
door - doNor

Solution:

An autobiography

Solution:

A parachute that didn't open.

Solution:

prinka is 10, in a system that awards five for each vowel.

Solution:

20
Just count the nines in the numbers: 6, 16, 26, 36, 46, 56, 76, 86, 96, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69.
Note: 66 contains TWO nines

Solution:

Ganpat had a black suit and a brown suit.
Harish had a brown suit and a pink suit.
Manoj had a white suit and a black suit.
Tarun had a pink suit and a white suit.

Solution:

'2'

This single sequence in fact consists of two Series:
The first Series is 2-3-4-5-...
and
The second Series is 9-18-36-72-... .

Solution:

Bill. If you read the message upside down, you'll notice that the numbers resemble letters and that those letters form legible sentences. The message is 'Bill is boss. He sells oil.'

Solution:

You can never solve a problem on the level on which it was created.

Here is the answer key:
A-Z
B-Y
C-X
D-W
E-V
F-U
G-T
H-S
I-R
J-Q
K-P
L-O
M-N
N-M
O-L
P-K
Q-J
R-I
S-H
T-G
U-F
V-E
W-D
X-C
Y-B
Z-A

Solution:

The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be 'changed' an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.

So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.