For some people, when I go to their FB profile, and click on their profile picture, it doesn't show any likes or comments. The right hand side where those things should be is just black. How do I make this happen? Related question : how do I change my profile picture without anyone knowing? I've seen other people change their profile picture and it didn't show up in my newsfeed.
Go to the post on your profile where it says you changed your profile picture. There is an arrow pointing down on the top right of the box that post is in. Click it and then click "hide from timeline". I dunno about the other thing. Sounds like a privacy setting. Go to your settings and look around.
Regarding the first question, Facebook had an update where even if the person's profile is private, any user can view their profile picture (not necessarily likes or comments unless the other user specifies in their personal settings).