What does this Rebus Picture mean?

I shave every day, but my beard stays the same. What am I?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

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

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

John and Jacob are twin brothers. One of them is a liar whereas the other one is a truth-teller.

I called their home number and one of them picked up.
I asked. 'Does John lie?' The person replied with a yes.

Whom did I talk with, John or Jacob?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

My cousin lives in one story house in Antarctica. His house is made the of-of sandstone. what is the color of stairs?

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

Can you find a number that lies one third of the distance between 1/3 and 2/3?