Sure! Here are the responses you can offer to the driver in a helpful manner using "Shall I":
The driver says he is thirsty.
- Shall I get you some water?
The driver would like you to send a message to his wife.
- Shall I send a message to your wife for you?
The driver is worried about some important papers in his briefcase.
- Shall I help you check your briefcase for those important papers?
The driver would like you to come and visit him in the hospital.
- Shall I come and visit you in the hospital?
The driver wonders if you could stay with his car till the breakdown truck comes.
- Shall I stay with your car until the breakdown truck arrives?
The driver asks you to look after his case which is in the boot.
- Shall I look after your case in the boot?
Feel free to modify these suggestions as needed!