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

I travel all around the world but always stay in the corner. What am I?

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?

How many times do a clock's hands overlap in a day ?

You want to boil a two-minute egg. If you only have a three-minute timer (hourglass), a four-minute timer and a five-minute timer, how can you boil the egg for only two minutes?

What goes through cities and fields, but never moves?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

What question can you never answer yes to?

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