1.

It is possible that fog will delay their departure until tomorrow.

may 

Their departure    until tomorrow. 

2.

It is essential for every passenger to carry a boarding card.

must 

A boarding card    every passenger. 

3.

"I bought nothing abroad", Rita told the customs officer.

she 

Rita told the customs officer    anything abroad. 
                                                        [ hadn't instead of had not is also correct ]

4.

"When I retire I'm going to sail to India!", he said.

he 

He announced that when    going to sail to India. 

5.

Bill advised the children to lock their bikes when they left them unattended.

your 

Bill said to the children, "You   
when you leave them unattended". 

6.

Taking the train doesn't cost as much as flying.

going 

Taking the train is    plane. 

7.

Peter didn't think I had read the map properly.

You 

Peter said, "  the map properly, have you?"
                        [ haven't instead of have not is also correct ]

8.

The ferry seems to be turning round and coming back.

if 

It looks    turning round and coming back. 

9.

Traffic jams are very time-wasting.

a 

Traffic jams    time. 

10.

"You will soon be a good driver if you follow my advice", said the instructor.

drive 

The instructor said I   if I followed his advice.