Good Riddles

Question: There was once three trees. The first tree did whatever the third tree did, and the third tree did what ever the second one does. What happens if tree number two gets cut down?

Question: I can run but never walk. Wherever I go, thought are close behind me.

What am I?

Question: No matter how much rain comes down on it it won't get any wetter.

What is it?

Question: I am a nice word composed of five letters, but the Romans would call me a numbers.

What am I?

Question: I tear paper but I'm not mad,
I wear a purse but it's not a fad.

Who am I?