Why are the profile pics on my facebook page all mixed up?

First I'll explain the cause and then the solution second.

Web browsers save some of the information that they download on your hard drive. It is called a cache. They do this to save the time of downloading the information again. It's also useful so that the server does not have to re-send out the information as they can only send out so much data at once. Sometimes, the information in the cache gets confused and it will pull up the wrong cache. In your case, it pulled up the wrong profile picture the 3 people.

There are two options to fix it. If you notice something wrong, you can do a hard refresh (covered in the first source). Otherwise, you might consider doing a full cache clear (which is covered in the first and second article). The full cache clear may log you out of some websites. Consider a full cache clear since you noticed problems with the cache.

This is a challenging question, and one that has intrigued me for a very long time.

It's possible, although I'm not convinced