If you're 8 feet away from a door and with each move you advance half the distance to the door. How many moves will it take to reach the door?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

If you drop me I’m sure to crack, but give me a smile and I’ll always smile back. What am I?

What came first, the chicken or the egg?

What goes through cities and fields, but never moves?

There is something which you can be arrested for attempting but not for successfully completing.

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

I look at you, you look at me I raise my right, you raise your left. What am I?

It spends most of its day eating white, but when it’s quick enough, it gets to eat fruit and sometimes some blue things. It’s in a dark room, where the walls are blue, it runs from a ghost that roams the halls and haunts it all the time. What is it?

With pointed fangs I sit and wait; with piercing force I crunch out fate; grabbing victims, proclaiming might; physically joining with a single bite. What am I?