What is the word or phrase?

Solve this tricky question. You are trapped in a forest. With you, you have a gun preloaded with two bullets in it. In front of you, there is a tiger, a leopard and a jaguar.

How do you survive?

I am soft and cuddly that soothe your heart. But, If you pick my last name I am going to tear you all apart. Who am I?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

What goes up but never comes down?

Which word does the below Plexor means ?

In Greek mythology, the Sphinx sat outside of Thebes and asked this riddle of all travellers who passed by. If the traveller failed to solve the riddle, then the Sphinx killed him/her. And if the traveller answered the riddle correctly, then the Sphinx would destroy herself. The riddle:

What goes on four legs in the morning, on two legs at noon, and on three legs in the evening?

Oedipus solved the riddle, and the Sphinx destroyed herself.

You board a train. The train will have to enter a tunnel soon. You are claustrophobic. Which place is the best for you to sit?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain