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:

5 leopard and one sheep

since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.

Solution:

The Winchester brothers - sam and dean

Solution:

Align the toothpicks to form TEN. Use one toothpick for each of the lines.

Solution:

13 + 11 + 6 = 30

Explanation
The trick is that you just need to rotate '9' to form '6'.

Solution:

The stranger said that he thought the room was his. If so, he must have had the keys to the room and thus he must not have knocked.

Solution:

7 Races.

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:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

I am word "Introvert"

Solution:

First fill the 8 liters jug complete - 4, 8, 0
Fill the 5 liters jug with 8 liters jug - 4, 3, 5
Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0
Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3
Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3
Fill the 5 liters jug from the 8 liters jug - 1, 6, 5
Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.