Solution:

Nightmare.

Explanation:
(K)night + mare (A mare is the female of a horse)

Solution:

It can be done in 8 moves as shown in the animated image below.

Solution:

The brain teaser can be solved as shown in the image below.

Solution:

+ 9 6 2 3 3
+ 6 2 5 1 3
===========
1 5 8 7 4 6

Solution:

118119

Explanation:
Number are generated as below
1 2
3 4
1 x 4 + 2 = 6 , 2 x 3 + 1 = 7 => 67

3 4
5 6
3 x 6 + 4 = 22, 4 x 5 + 3 = 23 = 2223

5 6
7 8
5 x 8 + 6 = 46, 6 x 7 + 5 = 47 = 4647

7 8
9 10
7 x 10 + 8 , 8 x 9 +7 = 7879

Based on above pattern, desired number will be calculated as :
9 10
11 12
9 x 12 + 10 = 118, 10 x 11 + 9 = 119 = 118119

Solution:

The code is 645
Explanation :
A) From Clues 1st and 2nd we know that one 9 is not in the code
B) From Clue 2nd we know that 9 3 and 8 are part of code
C) From Clue 3rd we know that 4 and 6 are part of code
D) From Clue 5th we know that 1 and 2 are not part of the code as we know 6 is part of the code and just 1 of 3 numbers is part of code.
E) From Clue 4th we know that 5 is also in the code as 8 and 1 are not part of code.

So the code is: 645

Solution:

They are all anagrams of time-related words.

1. CHARM: MARCH
2. DYNAMO: MONDAY
3. YAM: MAY
4. REAY: YEAR
5. EAR: ERA
6. ONE: EON
7. TOADY: TODAY

Solution:

NUMBER +
NUMBER
=======
PUZZLE

Above puzzle can be solved by substituting
N - 2
U - 0
M - 1
B - 6
E - 8
R - 9
P - 4
Z - 3
L - 7

The puzzle can now be read as:

201689 +
201689
----------
403378

Solution:

Step1 : Mr.Hinx and Supermodel1, Mr.Hinx back
Step2 : Mr.Hinx and Supermodel2, Mr.Hinx back
Step3 : Blofeld and JamesBond, Blofeld back
Step4 : Mr.Hinx and Secret Diary, Mr.Hinx back
Step5 : Mr.Hinx and Blofeld, Mr.Hinx back
Step6 : Mr.Hinx and secretary1, Mr.Hinx back
Step7 : Mr.Hinx and secretary2

Solution:

There can be two possible solutions as shown in the picture below.

1,19,3,12,16,14,18,10,7,6,15,2,5,9,13,17,8,11,4
1,19,3,18,16,14,12,4,13,6,9,8,17,15,7,5,2,11,10