Riddle me this

Riddle me this

   

  Riddles are puzzling questions to be solved.Can you guess the answers to these three riddles? Some of them are easier than others.Give it a go and have fun!

1.  Everybody has one.
If you remove the first letter, a bit remains.
If you remove the second, bit still remains.
After much trying, you might be able to remove 
the third one also, but it remains. It dies hard!

2.  Big as a biscuit, deep as a cup, even a river can't fill it up. What is it?

3.  A man who lives on the tenth floor takes the lift down to the first floor every morning and goes to work. When  he comes back from work on a rainy day, or if there are other people in the lift, he goes to his floor directly. Otherwise, he goes to the seventh floor and walks up three floors to his flat.

Why does the man do this?