Solution:

The next three digits will be 138, 150 and 180.

If you analyze, you will find that all the numbers are increasing in order and are surrounded by two prime numbers.

For example, 4 is surrounded by 3 and 5; both are prime numbers.
6 is surrounded by 5 and 7; both are prime numbers.

Solution:

Bond was suspicious of the women as one never knocks its own door at the hotel.

Solution:

If two widows, each having a son married the son of the other widow, and then by the consummation of marriage, both the couples had a daughter, all the aforementioned relationships will turn to be true.

Solution:

192

Explanation:
I started with the number 192.
Adding the reversed 291 to 192 gave me 483.
Similarly,
483 + 384 = 867
867 + 768 = 1635
1635 + 5361 = 6996

Solution:

The woman told him to take out one nut each from the rest of the wheels and use them.

Solution:

Pages 19, 20, 23, 37, 38, & 42 will also be missing

Solution:

   9567
+ 1085
======
 10652

Solution:

You will ask, I have a number in my mind that i.e. either 2 or 3. Is the number that I have in my mind smaller or equal to the number that you are thinking of?

If Alan replies with no, he is thinking of the number 1.
If Alan replies with yes, he is thinking of the number 3.
If Alan replies with don't know, he is thinking of the number 2.

Solution:

Solution is shown in image below

Solution:

One Night Stand.

Explanation:
Number 'One' + Knight(chess piece) + st + and(symbol &)

Solution:

The attached picture gives away the solution. If you can find another solution, do send us yours.