Solution:

Terry was born in the Southern Hemisphere.

Solution:

A cigar stuck in the wall

Solution:

The clerk said that every day the password is CHANGED. Changed is the password.

Solution:

The mules is moving in circular path and hence outside legs travels more distance than inner legs.

Solution:

It can be down as shown below.

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.

Solution:

Rhea will open just one present.
Cindy|Y - Y is the 25th alphabet
Duk|E - E is the 5th alphabet
Joh|N - N is the fifteenth alphabet
Rhe|A - A is the first alphabet

Solution:

It can surely be true because it is not mentioned that it was raining.

Solution:

   9567
+ 1085
======
 10652

Solution:

7, 4, 6, 5, 8

Solution:

This puzzle has no answer if you are considering this figure in a 2d domain. However if you follow it on a three-dimensional plane, you can do it like shown in the figure given.