In the other countries I lived in having ID card is considered the most normal thing in the world. People would not imagine there are countries without id cards.
How does a person prove his/her identity without identity card?
Passport or driving licence? Many don't have them.

To prove my identity or address here I was asked 1) my mother's name, 2) my gas bill. They don't prove my identity or my address.

So, how does a person prove his/her identity without id card?
He doesn't.