What is more useful when it is broken?

Can you name an animal whose killing cannot be performed without spilling your own blood?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

I have branches, but no fruit, trunk or leaves. What am I?

Katrina wants to go on a date and prefers her date to be tall, dark and handsome.

Of the preferred traits - tall, dark and handsome - no two of Shahrukh, Ajay, Salman and Akshay have the same number.
Only Shahrukh or Akshay is tall and fair.
Only Ajay or Salman is short and handsome.
Shahrukh and Salman are either both tall or short.
Ajay and Akshay are either both dark or both fair.
Who is Katrina's date?

Intelligence Agency need to break the vault but the problem is that they are not able to break the vault.

On the vault, a text is written as:

31 11 33 33 43 45
21 25
31 24 11 31 51 41

To Break the code Intelligence Agency brings a mathematician named Joseph.
Minutes later he deciphers the code.

Whats the code?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

I am quite hot but become too cold if you remove the first two letters. What am I?

Make a sentence consisting of three words that have the whole alphabet.

A boy and his father are caught in a traffic accident, and the father dies. Immediately the boy is rushed to a hospital, suffering from injuries. But the attending surgeon at the hospital, upon seeing the boy, says 'I cannot operate. This boy is my son.' How is this situation explained?