When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

What has many keys but can’t open a single lock?

I sleep during the day and fly at night, but I have no feathers to aid my flight. What am I?

I am dry when I go inside, but wet when I am pulled outside.
The longer I am inside, the stronger I get
When I am completely out, I am wet and I literally sag
Who am I?

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

I came first on earth but second on the heaven.
I also came twice in a week but found just once in a year.
I stay away from months but you can find me in February.

What am I?

Without looking at a calendar, within a minute name, a boy's name using 5 consecutive 1st letters of 5 consecutive months

He digs out tiny caves and stores gold and silver in them. He also built bridges of silver and made crowns of gold. They are the smallest you could imagine. Sooner or later everybody needs his help, yet many people are afraid to let him help them. Who is he?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

What is more useful when it is broken?