Solution:

The sun is a star.

Explanation:
Let us find out how we got there.

- Substitute a word with its antonym.
The pound is not a start.

- Eliminate one letter from one word.
The pound is not a star.

- Remove one word.
The pound is a star.

- Take out a letter and insert another in its place.
The sound is a star.

- Take out two letters from one word.
The sun is a star.

Solution:

Daughter.

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:

   9567
+ 1085
======
 10652

Solution:

Since the knife was in her hand which implies that she was planning to kill her husband "Inspector Montalbano".

Solution:

The husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

The receptionist was pretty clever she played with the mute button of the phone while talking with her mother. She muted everything except the word emergency, call and help. So while talking, she sounded like 'Emergency… Call… Help' to her mother and thus she called the police.

Solution:

Upon reaching each room, he found out that the window facing the dead body was closed. He had to open the window himself. This tells that there was somebody else with him who closed the window. If he would have committed suicide, at least one window would have been open.

Solution:

2 degree below zero

Solution:

To do it, the marbles must be arranged as the vertices of an octahedron. If you are unsure, check the image below.