Solution:

This riddle is perspective riddle where reader perspective determines if it's a murder or suicide.

A) Evidence suggests its a Murder
1. There are many signs that suggest struggle in the room.

2. The dead man seems to be left handed as all the essential things like the glass of water, the laptop is placed on the left-hand side and the murderer not knowingly that man was a left-handed placed gun on the right side.

3. We can see a man running in the background and probably run after opening the window.

B) Evidence suggests its a Suicide
The guy was frustrated and bankrupt(In the picture we can see some sort of financial data which going down like anything). He got drunk. and smacked the bottle into the wall with frustration and threw everything on the floor.
He then writes a suicide note and placed it on the table.
Pulls out a gun and shoot himself.
Note: Also about the man running, fingerprint and man running direction does not match

My perspective answer: Its a murder.

Solution:

Number 3

Explanation:
Since it's a ladies bathroom, so only ladies can enter the bathroom and hence most likely the killer.

Solution:

Costa

Explanation:
c + 1 characters-> d
o + 2 characters-> q
s + 3 characters-> v
t + 4 characters-> x
a + 5 characters-> f

=> dqvxf = costa

Solution:

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

Solution:

The numbers that have been written over the calendar are:
12, 4, 8 and 3

A few numbers have been circled under particular months. The curious thing is that the numbers that have been written are the same number of corresponding months under which the dates have been marked.

What we can judge by the overall calendar is that the dates that have been marked may refer to the letters at that position in the month's name. In addition, the written numbers can be the position of those letters. Let's simplify below:

12th month is December
The number marked under December = 5
The fifth letter of December = M

4th month is April
The number marked under April = 4
The fourth letter of April = I

8th month is August
The number marked under August is 6
The sixth letter of August = T

3rd month is March
The numbers marked under March are 4 and 5
The fourth and fifth letter of March = C and H

When you combine the letters, you get the name as MITCH.
Therefore, Mitch is the killer.

Solution:

Maths Teacher

Explanation:
How can she give grades on the 1st day of the college?

Solution:

The murderer is Marcus.

The notes hinted towards the name of Marcus. How?
Just take the first letter from Compound, Art Room, Restroom, Underwater Room, Study Room and Movie Room and you will get:

C, A, R, U, S and M.

Rearranging these words leads to the name Marcus who is the murderer.

Solution:

The murderer is Jack.

Christopher is the seer so exclude him.
Now, if Danny was murderer, then Garry should have been killed.
Now we know that Garry was blocked. Therefore he cannot be the murderer.
Harry can't be the killer as he was killed himself.
This leaves with Jack.

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:

The guy threw a boomerang in the air from his window. It flew away and looped around to return back with high velocity. It hit his head and he died on the spot due to the injury. This can be the only logical explanation.