Solution:

3^2 = 4 + 5
(^ is used for squaring the term, it is not used here as a mathematical symbol.)

Solution:

It is simple. The sheriff never told him where the crime scene was. But still he reached at the right place. This points towards the fact that he knew it already and that he is the killer himself.

Solution:

The wife booked a two way ticket for herself and booked a one way ticket for her husband.

Solution:

There are only four cats. The room is too small and each cat is sitting at the tail of other.

Solution:

It is perfectly possible. The sailors were looking across the deck at each other and not at the sea.

Solution:

The person should say, "I will be burned alive".

Solution:

Only one(dead one)

other flew away :--)

Solution:

2

Solution:

2/13

There 4 kings & 4 jacks, which implies there are 8 cards that can satisfy the above problem.
=>8/52
=> 2/13

Solution:

G = 'Roger Federer'
H = 'Rafael Nadal'

#A spoke the truth and the rest lied.