Good Riddles

Question: If a mountain climber climbed up a mountain one day from midnight to midnight the next day and does the same thing the following day when coming down the mountain, would there be a time at which he was at the same position on the mountain both day?

Question: To look cool wrap me around your head.
Remove a letter and eat me instead.

What am I?

Question: I climb to the top I dive below I return again For another show.

Question: I go into the water red and come out black.

What am I?

Question: If you lose one of me, you are upset, bewildered, and perplexed.
If you lose two of me, you are blissfully unaware.

What am I?