Solution:

8m

Explanation:
From green bar, it's clear that
the height of vertical bar = 2/3 of uninterrupted shadow length

Therefore shadow of 6m of red bar indicates the height of 4m.
The remaining red bar casts a direct 1:1 vertical projection on the wall.

Therefore total length = 4m + 4m = 8m.

Solution:

The hidden cat is circled below.

Solution:

40

Explanation:
A) 123 + 0 = 16
20 - (1+3)

B) 234 + 0 = 24
30 - (2+4)

C) 345 + 0 = 32
40 - (3+5)

Then
456 + 0 = 40
50 - (4+6)

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:

As the balloon lost altitude, all of the thieves took off their clothes in order to decrease the overall weight. but when balloon continues to lose the attitude they decide one of them need to jump to the desert to decrease the weight.
The man who must jump is decided by the famous death game where one who picks the shortest toothpick must die.
Frank Catton pick the half toothpick and was already naked and hence the hence explain his state in the desert.

Solution:

Number 3

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

Solution:

It can be done as shown in the picture below. Key to solving such problems is to fill the prime number first.

Solution:

yaM

Explanation:
voN luJ ? raM beF

Step-1: Reversing the input text gives us:
Feb Mar ? Jul Nov

Step-2: Replace by month numbers
2 3 ? 7 11

Step-3: Find the relation
They all are prime numbers, the missing number here is "5".

Step-4:
5th month is May and reverse of May is yaM (answer)

Solution:

They are matched as shown in the picture below.

Solution:

The node can be connected as shown.