When a stranger (i.e. person who is not my Facebook friend) opens my personal Facebook URL (i.e. https://www.facebook.com/myusername/), several posts on my timeline are displayed. How can I ensure that nothing is displayed on my timeline in this case?
You need to go to those posts and change their visibility level. They're probably marked "public", which shows a globe icon. You need to click that and change the visibility to "Friends only" or whatever else is appropriate.