Solution:

Terry was in the lift.

Solution:

She is near the trunk of the tree as shown below.

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:

A coconut.

Explanation:
Thirsty: she can drink coconut water.
Hungry she can eat coconut's malai.
Cold: she can burn the cover of the coconut.

Solution:

8/(1−1/5)

Solution:

The node can be connected as shown.

Solution:

They are matched as shown in the picture below.

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:

Number 3

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

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.