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:

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

Solution:

The node can be connected as shown.

Solution:

888

Explanation:
Part-1: Triangle
The triangle is an equilateral triangle.
The value of E and L is determined by the position in the English alphabets i.e E = 5 & L = 12. Together they form number 512

As we know that the equilateral triangle has 3 equal sides, therefore
X^3 = 512
X = 8
=> XXX = 888 ... (desired)

Part-1: X/3 = X
X is the 24th letter, therefore 24/3 = 8

Solution:

A

Explanation:
Pi = 3.141592653.....
All images are related by pi value i.e "The number of straight lines on each shape corresponds to the digits of pi."

Solution:

Terry was in the lift.

Solution:

Treasure Map Is Hidden Inside The Hanging Room Floor.

Explanation.
Just reverse the text "roolF mooR gnignaH ehT edisnI neddiH sI paM erusaerT".

Solution:

TIF56

Explanation:
The password is formed as:
T (5th letter of Shruti)
I (5th letter of Arshika)
F(1st letter of Friday)
5(5th day of week)
6(Length of Friday)

Similarly, we will pick the 1st letter for Monday and 3rd letter for Wednesday.

Solution:

1000$ - (Profit he earned in antique watch)

Solution:

Congratulations

Explanation:
Message Was: Company Piano Numb Dining Racial Mozetta Traitor Meou Legacy Quintana Trick Missi Orange Frozen Sapphire

Pick the 1st letter of the first word, 2nd letter of the second word, Pick 1st letter from the third word and so on.

Company - C
Piano - O
Numb - N
Dining - G
Racial - R
Mozetta - A
Traitor - T
Meou - U
Legacy - L
Quintana - A
Trick - T
Missi - I
Orange - O
Frozen - N
Sapphire - S