People put me on the table and cut me but do not eat me. What am I?

In which direction should the missing arrow point?

It has five wheels, though often think four, You cannot use it without that one more, You can put things in it, you can strap things on top, You can't find it in the market, but you can still go shop. What is it?

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

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

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

I taste better than I can smell. Who am I?

I have a head like a cat and feet like a cat, but I am not a cat. What am I?