I am a boy of 13 years old. There is no room in the taxi. Can I sit on my mother's lap?

Yes, although you are 13 years old, you are still a child, and it is totally ok to sit on your mother's lap in a taxi. Although you are 13 years old, you are still a child in front of your mother and you need someone to take care of you. Since you are a child, of course you can sit on your mother's lap, and there are not many people in the taxi, just a few people. If you sit on your mother's lap without a seat, they all know it's because there is no seat.