Q: Do you have to stay to the right (automatically lane change to the right lane without being instructed to do so?)
Answer: No! During the road test there is a set route (or routes). The examiner will direct you where to go very clearly. If there are no instructions, it means go straight or follow the road, whichever comes first.
Having said that, examiners do want to see your skill level and encourage drivers to do things they might do in real life, such as lane change to move around a left-turning vehicle for example.
In BC it is law that vehicles keep to the right lane except to pass while driving on a highway or freeway only. When driving on city streets you may drive in the left lane if you want, regardless of being faster than the car beside you.